GED Math : Finding Slope and Intercepts

Example Questions

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Example Question #1 : Finding Slope And Intercepts

Find the slope and y-intercept of the line depicted by the equation:

Explanation:

The equation is written in slope-intercept form, which is:

where  is equal to the slope and  is equal to the y-intercept. Therefore, a line depicted by the equation

has a slope that is equal to and a y-intercept that is equal to .

Example Question #2 : Finding Slope And Intercepts

Find the slope and y-intercept of the line that is represented by the equation

Explanation:

The slope-intercept form of a line is: , where  is the slope and is the y-intercept.

In this equation, and

Example Question #3 : Finding Slope And Intercepts

The grade of a road is defined as the slope of the road expressed as a percent as opposed to a fraction or decimal.

Explanation:

The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is . Multiply this by 100% to get its equivalent percent:

This is the correct choice.

Example Question #4 : Finding Slope And Intercepts

Refer to above red line. What is its slope?

Explanation:

Given two points, , the slope can be calculated using the following formula:

Set :

Example Question #1 : Finding Slope And Intercepts

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

Explanation:

Convert the equation into slope-intercept form, which is , where  is the slope and  is the y-intercept.

Example Question #6 : Finding Slope And Intercepts

What is the slope of the line perpendicular to ?

Explanation:

In order to find the perpendicular of a given slope, you need that given slope!  This is easy to compute, given your equation.  Just get it into slope-intercept form.  Recall that it is

This means that your perpendicular slope (which is opposite and reciprocal) will be .

Example Question #1 : Finding Slope And Intercepts

What is the equation of a line with a slope perpendicular to the line passing through the points  and ?

Explanation:

First, you should solve for the slope of the line passing through your two points.  Recall that the equation for finding the slope between two points is:

Now, recall that perpendicular slopes are opposite and reciprocal.  Therefore, the slope of your line will be .   Given that all of your options are in slope-intercept form, this is somewhat easy.  Remember that slope-intercept form is:

is your slope.  Therefore, you are looking for an equation with

The only option that matches this is:

Example Question #8 : Finding Slope And Intercepts

What is the x-intercept of ?

No x-intercept

Explanation:

Remember, to find the x-intercept, you need to set  equal to zero.  Therefore, you get:

Simply solving, this is

Example Question #9 : Finding Slope And Intercepts

Find the slope of the line that has the equation:

Explanation:

Step 1: Move x and y to opposite sides...

We will subtract 2x from both sides...

Result,

Step 2: Recall the basic equation of a line...

, where the coefficient of y is .

Step 3: Divide every term by  to change the coefficient of y to :

Step 4: Reduce...

Step 5: The slope of a line is the coefficient in front of the x term...

So, the slope is

Example Question #10 : Finding Slope And Intercepts

Find the slope of the following equation: