All GED Math Resources
Example Questions
Example Question #2 : Parallel And Perpendicular Lines
Consider the equations and . Which of the following statements is true of the lines of these equations?
The lines are parallel.
The lines are perpendicular.
The lines are distinct but neither parallel nor perpendicular.
The lines are one and the same.
The lines are perpendicular.
We find the slope of each line by putting each equation in slope-intercept form and examining the coefficient of .
is already in slope-intercept form; its slope is .
To get into slope-intercept form we solve for :
The slope of this line is .
The slopes are not equal so we can eliminate both "parallel" and "one and the same" as choices.
Multiply the two slopes together:
The product of the slopes of the lines is , making the lines perpendicular.
Example Question #771 : Geometry And Graphs
Give ths slope of a line parallel to the line in the above figure.
In order to move from the lower left plotted point to the upper right plotted point, it is necessary to move up five units and right three units. This is a rise of 5 and a run of 3. The slope is the rise-to-run ratio, so the slope of the line is . Any line parallel to this line will have the same slope, so the correct response is .
Example Question #771 : Geometry And Graphs
Give the slope of a line perpendicular to the line in the above figure.
In order to move from the lower left point to the upper right point, it is necessary to move up five units and right three units. This is a rise of 5 and a run of 3. The slope of a line is the ratio of rise to run, so the slope of the line shown is .
A line perpendicular to this will have a slope equal to the opposite of the reciprocal of . This is .
Example Question #11 : Parallel And Perpendicular Lines
Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. What is the equation of that line in slope-intercept form?
First, we need to find the slope of the above line.
The slope of a line. given two points can be calculated using the slope formula:
Set :
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be .
Since we want the line to have the same -intercept as the above line, which is the point , we can use the slope-intercept form to help us. We set
, and solve for :
Substitute for and in the slope-intercept form, and the equation is
.
Example Question #13 : Parallel And Perpendicular Lines
Which of the following equations is represented by a line perpendicular to the line ?
The equation can be rewritten as follows:
This is the slope-intercept form, and the line has slope .
The line therefore has slope . Since a line perpendicular to this one must have a slope that is the opposite reciprocal of , we are looking for a line that has slope .
The slopes of the lines in the four choices are as follows:
:
:
:
: This is the correct choice.
Example Question #13 : Parallel And Perpendicular Lines
Given the following equation, what is the slope of the perpendicular line?
Subtract from both sides.
The slope of this line is negative three.
The slope of the perpendicular line is the negative reciprocal of this slope.
The answer is:
Example Question #1741 : Ged Math
Which line is parallel to the following:
Two lines are parallel if they have the same slope. Now, we know the slope-intercept form is written as follows:
where m is the slope and b is the y-intercept. Now, given the equation
we can see the slope is -3. So, to find a line parallel to this line, we will have to find an equation that also have a slope of -3.
If we look at the equation
we can see it has a slope of -3. Therefore, this equation is parallel to the original equation.
Example Question #71 : Coordinate Geometry
Find a line that is perpendicular to the following:
Two lines are perpendicular if their slopes have opposite signs (positive/negative) and they are reciprocals of each other.
To find a reciprocal of a number, we will write it in fraction form. Then, the numerator becomes the denominator and the denominator becomes the numerator. In other words, we flip the fraction.
We will look at the lines in slope-intercept form
where m is the slope and b is the y-intercept.
So, given the equation
we can see the slope is . Now, the opposite reciprocal of this slope is which is the same as . So, we will find the equation that has as the slope.
So, in the equation
we can see the slope is . Therefore, it is perpendicular to the original equation.
Example Question #71 : Coordinate Geometry
Find a line that is parallel to the following line:
Two lines are parallel if they have the same slope. So, we will look at the lines in slope-intercept form:
where m is the slope and b is the y-intercept.
So, given the line
we can see the slope is -2. So, to find a line that is parallel, it must also have a slope of -2. So, the line
we can see it also has a slope of -2. Therefore, it is parallel to the original line.
Example Question #72 : Coordinate Geometry
If a line has a slope of , what must be the slope of the perpendicular line?
The perpendicular line slope will be the negative reciprocal of the original slope.
Substitute the given slope into the equation.
The answer is: