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Example Questions
Example Question #1 : How To Find The Slope Of A Line
Refer to the following graph:
What is the slope of the line shown?
3
–1/3
–1
1/3
–3
–3
One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m. By calculation or observation, one can determine that the slope is –3.
Example Question #1 : How To Find The Slope Of A Line
What is the slope of the equation 4x + 3y = 7?
–3/4
4/3
3/4
–4/3
–7/3
–4/3
We should put this equation in the form of y = mx + b, where m is the slope.
We start with 4x + 3y = 7.
Isolate the y term: 3y = 7 – 4x
Divide by 3: y = 7/3 – 4/3 * x
Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.
Example Question #1 : How To Find The Slope Of A Line
What is the slope of the equation ?
To find the slope of a line, you should convert an equation to the slope-intercept form. In this case, the equation would be , which means the slope is
.
Example Question #1 : How To Find The Slope Of A Line
What is the slope of the line ?
To find the slope, put the equation in slope-intercept form . In this case we have
, which indicates that the slope is
.
Example Question #1 : How To Find The Slope Of A Line
What is the slope of a line passing through the point
, if it is defined by:
?
Since the equation is defined as it is, you know the y-intercept is . This is the point
. To find the slope of the line, you merely need to use the two points that you have and find the equation:
Example Question #1 : How To Find The Slope Of A Line
Which of the following could be an equation for the red line pictured above?
There are two key facts to register about this drawing. First, the line clearly has a negative slope, given that it runs "downhill" when you look at it from left to right. Secondly, it has a positive y-intercept. Therefore, you know that the coefficient for the term must be negative, and the numerical coefficient for the y-intercept must be positive. This only occurs in the equation
. Therefore, this is the only viable option.
Example Question #1 : How To Find The Slope Of A Line
What is the slope of a line defined by the equation:
A question like this is actually rather easy. All you need to do is rewrite the equation in slope intercept form, that is:
Therefore, begin to simplify:
Becomes...
Then...
Finally, divide both sides by :
The coefficient for the term is your slope:
Example Question #1 : How To Find The Slope Of A Line
What is the slope of line 3 = 8y - 4x?
0.5
-0.5
-2
2
0.5
Solve equation for y. y=mx+b, where m is the slope
Example Question #1 : How To Find The Slope Of A Line
Find the slope of the line 6X – 2Y = 14
12
-3
-6
3
3
Put the equation in slope-intercept form:
y = mx + b
-2y = -6x +14
y = 3x – 7
The slope of the line is represented by M; therefore the slope of the line is 3.
Example Question #32 : Lines
If 2x – 4y = 10, what is the slope of the line?
2
0.5
–0.5
–2
–5/2
0.5
First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.
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