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Precalculus : Graph a Linear Function

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Example Questions

Example Question #1 : Graph A Linear Function

Which of the following could be the function modeled by this graph?

Linearfxn

Possible Answers:

y=7x-5

y=5x-7

y=5x+7

$y=\frac{1}{5}x-7$

Correct answer:

y=5x-7

Explanation:

Which of the following could be the function modeled by this graph?

Linearfxn

We can begin here by trying to identify a couple points on the graph

We can see that it crosses the y-axis at (0,-7)

Therefore, not only do we have a point, we have the y-intercept. This tells us that the equation of the line needs to have a in it somewhere. Eliminate any option that do not have this feature.

Next, find the slope by counting up and over from the y-intercept to the next clear point.

It seems like the line goes up 5 and right 1 to the point (1,-2)

This means we have a slope of 5, which means our equation must look like this:

y=5x-7

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Example Question #1 : Graph A Linear Function

Find the slope of the linear function

y-3=5(x+2)

Possible Answers:

m=3

m=-3

m=5

m=2

Correct answer:

m=5

Explanation:

For the linear function in point-slope form

$y-y_{1}=m\left ( x-x_{1}\right )$

The slope is equal to

For this problem

y-3=5(x+2)

we get

m=5

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Example Question #1 : Graph A Linear Function

Find the slope of the linear function

y-7=10(x+1)

Possible Answers:

m=10

m=-7

m=7

m=1

Correct answer:

m=10

Explanation:

For the linear function in point-slope form

$y-y_{1}=m\left ( x-x_{1}\right )$

The slope is equal to

For this problem

y-7=10(x+1)

we get

m=10

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Example Question #3 : Linear Functions

What is the y-intercept of the line below?

y = 3x + 4

Possible Answers:

(3,0)

(0, 4)

(4,0)

(0, -3)

(0, 3)

Correct answer:

(0, 4)

Explanation:

By definition, the y-intercept is the point on the line that crosses the y-axis. This can be found by substituting x = 0 into the equation. When we do this with our equation,

$y = 3x + 4 = 3\cdot0 + 4 = 0 + 4 = 4$ .

Alternatively, you can remember y = mx + b form, a general form for a line in which is the slope and is the y-intercept.

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Example Question #4 : Linear Functions

What is the slope of the line below?

$y = \frac{2}{3}x + 6$

Possible Answers:

$\frac{1}{6}$

$-\frac{2}{3}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

Recall slope-intercept form, or y = mx + b . In this form, is the slope and is the y-intercept. Given our equation above, the slope must be the coefficient of the x, which is $\frac{2}{3}$ .

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Example Question #5 : Linear Functions

What is the x-intercept of the equation below?

y = 3x - 6

Possible Answers:

(0, -6)

$(\frac{1}{2}, 0)$

(-2, 0)

(0, 2)

(2,0)

Correct answer:

(2,0)

Explanation:

The x-intercept of an equation is the point at which the line crosses the x-axis. Thus, we can find the x-intercept by plugging in y=0 . When we do this with our equation:

$y = 3x - 6 \rightarrow 0 = 3x - 6\rightarrow6 = 3x \rightarrow2 = x$

Thus, our x-intercept is the point (2,0) .

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Precalculus : Graph a Linear Function

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Graph A Linear Function

Example Question #1 : Graph A Linear Function

Example Question #1 : Graph A Linear Function

Example Question #3 : Linear Functions

Example Question #4 : Linear Functions

Example Question #5 : Linear Functions

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