### All Common Core: 8th Grade Math Resources

## Example Questions

### Example Question #1 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

A line has the equation . What is the slope of this line?

**Possible Answers:**

**Correct answer:**

You need to put the equation in form before you can easily find out its slope.

Since , that must be the slope.

### Example Question #2 : How To Find Slope

The equation of a line is . Find the slope of this line.

**Possible Answers:**

**Correct answer:**

To find the slope, you will need to put the equation in form. The value of will be the slope.

Subtract from either side:

Divide each side by :

You can now easily identify the value of .

### Example Question #1 : How To Find X Or Y Intercept

What is the -intercept of the graph of the function ?

**Possible Answers:**

**Correct answer:**

The -intercept of the graph of a function is the point at which it intersects the -axis - that is, at which . This point is , so evaluate :

The -intercept is .

### Example Question #4 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Give the -intercept, if there is one, of the graph of the equation

**Possible Answers:**

The graph has no -intercept.

**Correct answer:**

The graph has no -intercept.

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

However, since this expression has 0 in a denominator, it is of undefined value. This means that there is no value of paired with -coordinate 0, and, subsequently, the graph of the equation has no -intercept.

### Example Question #1 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Give the -intercept, if there is one, of the graph of the equation

**Possible Answers:**

The graph has no -intercept.

**Correct answer:**

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

The -intercept is .

### Example Question #2 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

.

**Possible Answers:**

The graph does not have a -intercept.

**Correct answer:**

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

The -intercept is the point .

### Example Question #271 : Geometry

A line passes through and is perpendicular to the line of the equation . Give the -intercept of this line.

**Possible Answers:**

The line has no -intercept.

**Correct answer:**

First, find the slope of the second line by solving for as follows:

The equation is now in the slope-intercept form ; the slope of the second line is the -coefficient .

The first line, being perpendicular to the second, has as its slope the opposite of the reciprocal of , which is .

Therefore, we are looking for a line through with slope . Using point-slope form

with

,

the equation becomes

.

To find the -intercept, substitute 0 for and solve for :

The -intercept is the point .

### Example Question #8 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

A line passes through and is parallel to the line of the equation . Give the -intercept of this line.

**Possible Answers:**

The line has no -intercept.

**Correct answer:**

First, find the slope of the second line by solving for as follows:

The equation is now in the slope-intercept form ; the slope of the second line is the -coefficient .

The first line, being parallel to the second, has the same slope.

Therefore, we are looking for a line through with slope . Using point-slope form

with

,

the equation becomes

.

To find the -intercept, substitute 0 for and solve for :

The -intercept is the point .

### Example Question #9 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Give the -intercept of the line with slope that passes through point .

**Possible Answers:**

The line has no -intercept.

**Correct answer:**

By the point-slope formula, this line has the equation

where

By substitution, the equation becomes

To find the -intercept, substitute 0 for and solve for :

The -intercept is the point .

### Example Question #10 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Give the -intercept of the line that passes through points and .

**Possible Answers:**

The line has no -intercept.

**Correct answer:**

First, find the slope of the line, using the slope formula

setting :

By the point-slope formula, this line has the equation

where

; the line becomes

or

To find the -intercept, substitute 0 for and solve for :

The -intercept is .