Algebra I

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Questions 1 - 10
1

Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points and .

Explanation

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula . Isolate for .

2

Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points and .

Explanation

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula . Isolate for .

3

What line is perpendicular to through ?

Explanation

Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

4

Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points and .

Explanation

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula . Isolate for .

5

What line is perpendicular to through ?

Explanation

Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

6

What line is perpendicular to through ?

Explanation

Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

7

A straight line passes through the points and .

What is the -intercept of this line?

Explanation

First calculate the slope:

The standard equation for a line is .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get .

Therefore, .

Our equation for the line is now:

To find the -intercept, we plug in :

Thus, the -intercept the point (4,0).

8

What line is perpendicular to through ?

Explanation

Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

9

A straight line passes through the points and .

What is the -intercept of this line?

Explanation

First calculate the slope:

The standard equation for a line is .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get .

Therefore, .

Our equation for the line is now:

To find the -intercept, we plug in :

Thus, the -intercept the point (4,0).

10

A straight line passes through the points and .

What is the -intercept of this line?

Explanation

First calculate the slope:

The standard equation for a line is .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get .

Therefore, .

Our equation for the line is now:

To find the -intercept, we plug in :

Thus, the -intercept the point (4,0).

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