Linear Functions

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Questions 1 - 10

1

Solve:

No solutions

Infinitely many solutions

Explanation

Use substution to solve this problem:

becomes and then is substituted into the second equation. Then solve for :

, so and to give the solution .

2

Solve:

No solutions

Infinitely many solutions

Explanation

Use substution to solve this problem:

becomes and then is substituted into the second equation. Then solve for :

, so and to give the solution .

3

Which of the following is a horizontal line?

Explanation

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

4

Which of the following is a horizontal line?

Explanation

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

5

Solve for the - and - intercepts:

$\left ( \frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

$\left ( -\frac{11}{5},0\right)\ and \left ( 0,\frac{11}{2}\right)$

$\left ( -\frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

$\left ( \frac{11}{5},0\right)\ and \left ( 0,\frac{11}{2}\right)$

Explanation

To solve for the -intercept, set to zero and solve for :

$x=\frac{11}{5}$

To solve for the -intercept, set to zero and solve for :

$y=-\frac{11}{2}$

6

Solve for the - and - intercepts:

$\left ( \frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

$\left ( -\frac{11}{5},0\right)\ and \left ( 0,\frac{11}{2}\right)$

$\left ( -\frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

$\left ( \frac{11}{5},0\right)\ and \left ( 0,\frac{11}{2}\right)$

Explanation

To solve for the -intercept, set to zero and solve for :

$x=\frac{11}{5}$

To solve for the -intercept, set to zero and solve for :

$y=-\frac{11}{2}$

7

Which of the following is a vertical line?

Explanation

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form , where is a real number. The only equation of this form is .

8

Which of the following is a vertical line?

Explanation

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form , where is a real number. The only equation of this form is .

9

Write in slope-intercept form.

$y=\frac{-2}{7}x+\frac{8}{7}$

$y=\frac{2}{7}x-\frac{8}{7}$

$y=\frac{-2}{7}x-\frac{8}{7}$

$y=\frac{2}{7}x+\frac{8}{7}$

Explanation

Slope-intercept form is .

$y=\frac{-2}{7}x+\frac{8}{7}$

10

Write in slope-intercept form.

$y=\frac{-2}{7}x+\frac{8}{7}$

$y=\frac{2}{7}x-\frac{8}{7}$

$y=\frac{-2}{7}x-\frac{8}{7}$

$y=\frac{2}{7}x+\frac{8}{7}$

Explanation

Slope-intercept form is .

$y=\frac{-2}{7}x+\frac{8}{7}$

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