### All GRE Math Resources

## 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?

**Possible Answers:**

–3

3

1/3

–1

–1/3

**Correct answer:**

–3

One can use either the slope formula m = (y_{2} – y_{1})/(x_{2} – x_{1}) 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 4*x* + 3*y* = 7?

**Possible Answers:**

4/3

–3/4

–7/3

3/4

–4/3

**Correct answer:**

–4/3

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

We start with 4*x* + 3*y* = 7.

Isolate the *y* term: 3*y* = 7 – 4*x*

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 ?

**Possible Answers:**

**Correct answer:**

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:**

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:

?

**Possible Answers:**

**Correct answer:**

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 : Other Lines

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

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

-0.5

-2

0.5

2

**Correct answer:**

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

**Possible Answers:**

12

-3

3

-6

**Correct answer:**

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 #2 : How To Find The Slope Of A Line

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

**Possible Answers:**

0.5

–2

–0.5

2

–5/2

**Correct answer:**

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.