All GED Math Resources
Example Questions
Example Question #1 : Finding Slope And Intercepts
Find the slope and y-intercept of the line depicted by the equation:
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
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.
A road is graded so that for every 40 feet of horizontal distance, the road rises 6 feet. What is the grade of the road?
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?
Given two points, , the slope can be calculated using the following formula:
Set :
Example Question #5 : Finding Slope And Intercepts
What is the slope and y-intercept of the following line?
Convert the equation into slope-intercept form, which is , where is the slope and is the y-intercept.
Example Question #5 : Finding Slope And Intercepts
What is the slope of the line perpendicular to ?
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
Simplifying your equation, you get:
This means that your perpendicular slope (which is opposite and reciprocal) will be .
Example Question #6 : Finding Slope And Intercepts
What is the equation of a line with a slope perpendicular to the line passing through the points and ?
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:
For your data, this 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 #6 : Finding Slope And Intercepts
What is the x-intercept of ?
No x-intercept
Remember, to find the x-intercept, you need to set equal to zero. Therefore, you get:
Simply solving, this is
Example Question #2 : Finding Slope And Intercepts
Find the slope of the line that has the equation:
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 #1 : Finding Slope And Intercepts
Find the slope of the following equation:
In order to find the slope, we will need the equation in slope-intercept form.
Distribute the negative nine through the binomial.
The slope is: