# GRE Math : How to find the slope of a line

## Example Questions

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### Example Question #211 : Geometry

Refer to the following graph:

What is the slope of the line shown?

–3

–1

1/3

3

–1/3

–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 #1 : How To Find The Slope Of A Line

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

–3/4

–7/3

4/3

3/4

–4/3

–4/3

Explanation:

We should put this equation in the form of y = mx + b, where m is the slope.

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 ?

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 ?

Explanation:

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:

?

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 #1 : How To Find The Slope Of A Line

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

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 #7 : How To Find The Slope Of A Line

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

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 #1 : How To Find The Slope Of A Line

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

2

0.5

-2

-0.5

0.5

Explanation:

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

3

12

-3

-6

3

Explanation:

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 #1 : How To Find The Slope Of A Line

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

–2

0.5

2

–0.5

–5/2