This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! The volume increases by 12 liters every 3 minutes, so rate = 12/3 = 4 liters per minute constantly, as it's a steady fill implying linear: V(t) = 4t (assuming starts at 0). Choice A correctly identifies the constant rate because the increase is proportional with fixed rate 4, a linear relationship. A distractor like choice D might see the ratio 12:3 and think it's constant ratio, but that's actually the rate (difference over interval)—distinguish by noting ratios would be for multiplicative growth, not additive here. The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! When a car travels at a steady speed of 55 miles per hour, this means for every 1 hour increase in time, the distance increases by exactly 55 miles: Δdistance/Δtime = 55 miles/hour constantly. This gives us the linear function d = 55t, where the slope 55 represents the constant rate of change. Choice A correctly identifies both the constant rate of 55 mph and that this makes the relationship linear. Choice B incorrectly thinks that because distance keeps increasing, the rate must change—but it's the amount of increase per hour that matters, not the total distance. Choice C wrongly labels it exponential when steady speed always produces linear relationships. The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Among the options, choice C (runner at steady 8 m/s) has constant rate: distance = 8 * time, linear with rate 8; whereas A is exponential decay (multiplicative), B is quadratic (area = side²), D is exponential growth (doubling). Choice C correctly identifies the constant rate because steady speed means fixed distance per time, a linear relationship. A distractor like choice D might seem constant but doubling is constant ratio, not rate—test by checking if changes add constantly or multiply. The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! For f(x)=3x²-6x+1, it's quadratic (degree 2, not 1), so the rate varies; for example, from x=0 to 1, Δf=(3-6+1)-(1)= -2 to -1? Wait, f(0)=1, f(1)=3-6+1=-2, Δf=-3; f(2)=12-12+1=1, Δf from 1 to 2=3—not constant. Choice B correctly identifies it as quadratic and thus non-constant rate because it's not in mx+b form. A distractor like choice A might misread the -6x term as the constant rate, but ignore the x² which makes the rate change—always check the highest degree for linearity! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! For Relationship 1: The differences are 9-7=2, 11-9=2, 13-11=2, giving constant Δy/Δx = 2/1 = 2 for all intervals—this is linear with constant rate! For Relationship 2: The differences are 4-2=2, 8-4=4, 16-8=8, giving rates of 2, 4, 8—these double each time, indicating exponential growth where y = 2^(x+1). The ratios are constant (4/2=2, 8/4=2, 16/8=2), but the rates vary. Choice C correctly identifies that only Relationship 1 has constant rate of change because its differences are constant, making it linear. Choice B confuses constant ratio (which characterizes exponential functions) with constant rate (which characterizes linear functions). The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 7 for one interval and also 7 for every other equal interval, the rate is constant at 7. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! The function f(x) = 7x - 3 is already in the form y = mx + b, where m = 7 is the slope (constant rate of change) and b = -3 is the y-intercept. This form immediately tells us the function is linear with a constant rate of change equal to the coefficient of x, which is 7. To verify, we can check: if x increases by 1, then f(x) increases by 7(1) = 7; if x increases by 2, then f(x) increases by 7(2) = 14, which is exactly 2 times the change for a unit increase. Choice B correctly identifies that the constant rate of change is 7, recognizing this as a linear function. Choice C incorrectly claims the rate is -3, confusing the y-intercept (the constant term) with the rate of change (the coefficient of x). The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. In the formula y = mx + b, m is the constant rate. In y = $ab^x$, b is the constant ratio. If neither form fits → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Situation (a) fills 4 gallons per minute, so constant Δgallons/Δtime=4, linear; (b) area A=s², rate dA/ds=2s varies with s, quadratic; (c) doubles hourly, constant ratio 2 but varying differences (e.g., 1 to 2, +1; 2 to 4, +2), exponential. Choice A correctly identifies only (a) as having constant rate because it's additive growth, equivalent to linear. For (c), a common error is thinking doubling is constant rate, but that's constant ratio—calculate differences to confirm they increase, not stay equal! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! The function f(x)=5x-2 is in y=mx+b form with m=5, so the slope (rate) is constantly 5 for any interval. Choice A correctly identifies the constant rate because it's linear with slope 5. A distractor like choice B might think the -2 affects the rate, but it's just the intercept—rate is the coefficient of x, which is unchanging. The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 3 for one interval but 5 for another, the rate is non-constant. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! For g(x) = x² + 2, let's calculate values and differences using Δx = 1: when x = 0, g(0) = 0² + 2 = 2; when x = 1, g(1) = 1² + 2 = 3; when x = 2, g(2) = 4 + 2 = 6; when x = 3, g(3) = 9 + 2 = 11. The differences are: Δg = 3-2 = 1, then 6-3 = 3, then 11-6 = 5. Since the differences (1, 3, 5) are not constant, the rate of change Δy/Δx varies, confirming this is nonlinear. Choice C correctly identifies that g(x) is quadratic, so Δy/Δx changes and the relationship is nonlinear. Choice A incorrectly thinks the +2 determines the rate of change, but in a quadratic function, the rate depends on x and is not constant—the +2 just shifts the parabola up. The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. For g(x) = x² + 2, the x² term makes it quadratic—the rate of change is 2x, which varies with x. Only functions of the form f(x) = mx + b have constant rate m. Knowing the formula structure immediately tells you whether the rate is constant!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! For this table, calculate rates: from x=1 to 2, Δy/Δx=(6-2)/1=4; x=2 to 3, (12-6)/1=6; x=3 to 4, (20-12)/1=8, so rates vary (4,6,8) and are non-constant. Choice A correctly identifies the non-constant rate because the differences increase, indicating nonlinear. A distractor like choice B might confuse constant Δy with constant rate, but here Δy varies (4,6,8)—ensure you divide by Δx and check if those quotients are equal. The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!