# GRE Subject Test: Math : Slope & Intercept

## Example Questions

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### Example Question #1 : Slope & Intercept

What is the slope and y-intercept of this line: ?

Explanation:

Step 1: Move the y-term to the other side. We will add 4y.

Step 2: Move the constant to the other side. We will subtract 12.

Step 3: Divide by the coefficient in front of the y term. In this question, we divide all terms by 4.

Step 4: Identify the slope and the y-intercept. The slope is the number that is in front of the x term, and the y-intercept is the number that comes after the x-term.

In this question, the slope is  and the y-intercept is

### Example Question #2 : Slope & Intercept

Find the slope of a line that passes through points  and .

Slope is undefined.

Explanation:

The formula for slope is:

When the y coordinates are the same, as in this case both were -1, this would form a horizontal line.  The slope of a horizontal line is zero.

### Example Question #3 : Slope & Intercept

Find the slope of a line that passes through points  and

Slope is undefined.

Slope is undefined.

Explanation:

The formula for slope is:

Slope is undefined.

If the x coordinates are the same, as in this problem both x coordinates are 4, then this will be a vertical line.  The slope of a vertical line is undefined.

### Example Question #4 : Slope & Intercept

Find the slope of a line that passes through points  and

Slope is undefined.

Explanation:

The formula for slope is:

### Example Question #5 : Slope & Intercept

What is the slope and y-intercept of the following equation?

and

and

and

and

and

Explanation:

Subtract  from both sides of the equation.

Write equation in the form of   .

( represents the y-intercept)

### Example Question #6 : Slope & Intercept

What is the slope () and the y-intercept  of the equation

and

and

and

and

and

Explanation:

The formula to find slope and y-intercept is:

and

### Example Question #7 : Slope & Intercept

What is the slope and the y-intercept  of the equation

and

and

and

and

and

Explanation:

The formula to find slope and y-intercept is:

Combine like terms.

and

### Example Question #8 : Slope & Intercept

The points given lie on a line. Find the slope.

Explanation:

slope   =

rise  =   changes in y

run  =   changes in x

The change in the  coordinates is that the numbers are decreasing by 3 or -3.

The change in the  coordinates is that the numbers are increasing by 2 or +2;

slope =

### Example Question #9 : Slope & Intercept

The points given lie on a line.  Find the slope.

Explanation:

slope  =

rise  =   changes in y

run  =   changes in x

The change in the  coordinates is that the numbers are increasing by 3 or +3.

The change in the  coordinates is that the numbers are increasing by 4 or +4.

slope =

### Example Question #10 : Slope & Intercept

The points given lie on a line. Find the slope.

Slope is undefined.

Explanation:

slope =

rise  =   changes in y

run  =   changes in x

There is zero change in the  coordinates.

The change in the  coordinates is that the numbers are increasing by 2 or +2.

slope =

If the   coordinates are the same, then it will be a horizontal line.  The slope of a horizontal line is 0.

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