# GED Math : Coordinate Geometry

## Example Questions

### Example Question #11 : X Intercept And Y Intercept

Find the x-intercept of the following equation:

Explanation:

Find the x-intercept of the following equation:

The x-intercept is the point where the line crosses the x-axis. At this point, the y-value must be 0.

To find the x-intercept, plug in "0" for y and solve for x.

Now finish up by dividing by 2:

We can check our answer by plugging it back into our equation:

Everything looks good, so our answer is -8.5

### Example Question #51 : Coordinate Geometry

The following points lie on a line.

What is the equation of the line?

Explanation:

Start by finding the slope of the line by using any two points.

Recall how to find the slope of a line:

Using the points , we can find the slope.

Now, we can write the following equation:

To find the value of , the y-intercept, plug in any point into the equation above. Using the point , we can write the following equation:

Thus, the complete equation for this line is .

### Example Question #761 : Geometry And Graphs

Find the x intercept of the following linear equation.

Explanation:

Find the x intercept of the following linear equation.

x intercepts occur when y=0, in other words, when we have no height.

So, plug in 0 for y and solve for x

So our x intercept is negative one half.

### Example Question #51 : Coordinate Geometry

Find the y intercept of the following linear equation.

Explanation:

Find the y intercept of the following linear equation.

The y-intercept occurs when x is 0. Find it by plugging in 0 for x and solving for y.

### Example Question #1 : Parallel And Perpendicular Lines

Which of the following equations depicts a line that is perpendicular to the line

?

Explanation:

The given equation is written in slope-intercept form, and the slope of the line is . The slope of a perpendicular line is the negative reciprocal of the given line. The negative reciprocal here is . Therefore, the correct equation is:

### Example Question #2 : Parallel And Perpendicular Lines

Which of the following equations is represented by a line perpendicular to the line of the equation  ?

Explanation:

The equation  can be rewritten as follows:

This is the slope-intercept form, and the line has slope

The line of the equation  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 with slope .

The slopes of the lines in the four choices are as follows:

- this is the correct one.

### Example Question #3 : Parallel And Perpendicular Lines

Which of the following equations is represented by a line perpendicular to the line of the equation  ?

Explanation:

can be rewritten as follows:

Any line with equation  is vertical and has undefined slope; a line perpendicular to this is horizontal and has slope 0, and can be written as . The only choice that does not have an  is , which can be rewritten as follows:

This is the correct choice.

### Example Question #52 : Coordinate Geometry

Which of the following equations is represented by a line perpendicular to the line of the equation  ?

Explanation:

The equation  can be rewritten as follows:

This is the slope-intercept form, and the line has slope

The line of the equation  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:

- the correct choice.

### Example Question #771 : Geometry And Graphs

Refer to the above red line. A line is drawn perpendicular to that line with the same -intercept. Give the equation of that line in slope-intercept form.

Explanation:

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 3, which would be . Since we want this line to have the same -intercept as the first line, which is the point , we can substitute  and  into the slope-intercept form of the equation:

### Example Question #6 : Parallel And Perpendicular Lines

Line  includes the points  and . Line  includes the points  and . Which of the following statements is true of these lines?

The lines are parallel.

The lines are identical.

The lines are distinct but neither parallel nor perpendicular.

The lines are perpendicular.

The lines are parallel.

Explanation:

We calculate the slopes of the lines using the slope formula.

The slope of line  is

.

The slope of line  is

.

The lines have the same slope, so either they are distinct parallel lines or one and the same line. One way to check for the latter situation is to find the slope of the line connecting one point on  to one point on  - if the slope is also , the lines coincide. We will use  and :

.

The lines are therefore distinct and parallel.