GRE Math : How to find the slope of a line

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #1 : How To Find The Slope Of A Line

Refer to the following graph:

Gre1

What is the slope of the line shown?

Possible Answers:

1/3

–3

–1/3

–1

3

Correct answer:

–3

Explanation:

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 #27 : Lines

What is the slope of the equation 4x + 3y = 7?

Possible Answers:

–3/4

3/4

4/3

–4/3

–7/3

Correct answer:

–4/3

Explanation:

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 #2 : How To Find The Slope Of A Line

What is the slope of the equation ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

To find the slope, put the equation in slope-intercept form . In this case we have y=-\frac{3}{2}+5, which indicates that the slope is .

Example Question #4 : How To Find The Slope Of A Line

What is the slope  of a line passing through the point , if it is defined by:

?

Possible Answers:

Correct answer:

Explanation:

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 #5 : How To Find The Slope Of A Line

Line1

Which of the following could be an equation for the red line pictured above?

Possible Answers:

Correct answer:

Explanation:

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 #6 : How To Find The Slope Of A Line

What is the slope of a line defined by the equation:

Possible Answers:

Correct answer:

Explanation:

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 #721 : Act Math

What is the slope of line 3 = 8y - 4x?

Possible Answers:

-0.5

0.5

2

-2

Correct answer:

0.5

Explanation:

Solve equation for y. y=mx+b, where m is the slope

Example Question #5 : How To Find The Slope Of A Line

Find the slope of the line  6X – 2Y = 14

 

Possible Answers:

-6

-3

3

12

Correct answer:

3

Explanation:

Put the equation in slope-intercept form:

y = mx + c

-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 #6 : How To Find The Slope Of A Line

If 2x – 4y = 10, what is the slope of the line?

Possible Answers:

–5/2

–0.5

2

0.5

–2

Correct answer:

0.5

Explanation:

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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