# Common Core: 8th Grade Math : Use Similar Triangles to Show Equal Slopes: CCSS.Math.Content.8.EE.B.6

## Example Questions

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### Example Question #4 : How To Find Slope

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

Explanation:

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

Since , that must be the slope.

### Example Question #6 : How To Find Slope

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

Explanation:

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

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

Explanation:

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 #2 : 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

The graph has no -intercept.

The graph has no -intercept.

Explanation:

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 #3 : How To Find X Or Y Intercept

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

The graph has no -intercept.

Explanation:

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 #4 : How To Find X Or Y Intercept

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

.

The graph does not have a -intercept.

Explanation:

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 #5 : How To Find X Or Y Intercept

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

The line has no -intercept.

Explanation:

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 #6 : How To Find X Or Y Intercept

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

The line has no -intercept.

Explanation:

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 #7 : How To Find X Or Y Intercept

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

The line has no -intercept.

Explanation:

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 #2 : 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 .

The line has no -intercept.

Explanation:

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 .

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