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High School Math : Linear Functions

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Example Questions

Example Question #1 : Linear Functions

Which of the following is a horizontal line?

Possible Answers:

x = 4

y=2x+1

y = 3x + 4

y = 0

y = -x

Correct answer:

y = 0

Explanation:

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form y = c , where is a constant. Horizontal lines have a slope of . The only equation of this form is y = 0 .

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Example Question #2 : Understanding Vertical And Horizontal Lines

Which of the following is a vertical line?

Possible Answers:

x = 3

y = x

y = 4

y = 3x + 2

$y = \frac{1}{x}$

Correct answer:

x = 3

Explanation:

A vertical line is one in which the values can vary. Namely, there is only one possible value for , and can be any number. Thus, by this description, the only vertical line listed is x = 3 .

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Example Question #2 : Understanding Vertical And Horizontal Lines

Which of the following has a slope of 0?

Possible Answers:

y = x

$y = 3^{x}$

y = 10

x = 0

$y = \frac{1}{x}$

Correct answer:

y = 10

Explanation:

A line with a slope of zero will be horizontal. A horizontal line has only one possible value for , and can be any value.

Thus, the only given equation which fits this description is y = 10 .

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Example Question #21 : Functions And Graphs

Which of the following is a vertical line?

Possible Answers:

x = 2

y = 6

y = 3x + 3

y = -x + 2

y = 0

Correct answer:

x = 2

Explanation:

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form x = c , where is a real number. The only equation of this form is x = 2 .

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Example Question #22 : Functions And Graphs

Solve for the - and - intercepts:

5x-2y=11

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

5x-2y=11

5x-2(0)=11

5x=11

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

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

5x-2y=11

5(0)-2y=11

-2y=11

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

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Example Question #23 : Functions And Graphs

Solve:

x+3y=10

-2x+y=1

Possible Answers:

(3,-2)

(-2,1)

No solutions

(1,3)

Infinitely many solutions

Correct answer:

(1,3)

Explanation:

Use substution to solve this problem:

x+3y=10 becomes x=10-3y and then is substituted into the second equation. Then solve for :

-2(10-3y)+y=1 , so y=3 and x=1 to give the solution (1,3) .

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Example Question #1 : Transformations Of Linear Functions

Write 2x+7y=8 in slope-intercept form.

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Slope-intercept form is y=mx+b .

2x+7y=8

7y=-2x+8

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

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High School Math : Linear Functions

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Linear Functions

Example Question #2 : Understanding Vertical And Horizontal Lines

Example Question #2 : Understanding Vertical And Horizontal Lines

Example Question #21 : Functions And Graphs

Example Question #22 : Functions And Graphs

Example Question #23 : Functions And Graphs

Example Question #1 : Transformations Of Linear Functions

All High School Math Resources

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