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

Determine where the graphs of the following equations will intersect.

Explanation

We can solve the system of equations using the substitution method.

Solve for in the second equation.

Substitute this value of into the first equation.

Now we can solve for .

$y=\frac{14}{-7}=-2$

Solve for using the first equation with this new value of .

$x=\frac{3}{3}=1$

The solution is the ordered pair .

3

Determine where the graphs of the following equations will intersect.

Explanation

We can solve the system of equations using the substitution method.

Solve for in the second equation.

Substitute this value of into the first equation.

Now we can solve for .

$y=\frac{14}{-7}=-2$

Solve for using the first equation with this new value of .

$x=\frac{3}{3}=1$

The solution is the ordered pair .

4

Determine where the graphs of the following equations will intersect.

Explanation

We can solve the system of equations using the substitution method.

Solve for in the second equation.

Substitute this value of into the first equation.

Now we can solve for .

$y=\frac{14}{-7}=-2$

Solve for using the first equation with this new value of .

$x=\frac{3}{3}=1$

The solution is the ordered pair .

5

Shift the graph down four units. What is the new equation?

$y=\frac{3}{2}x-2$

$y=\frac{3}{2}x$

$y=\frac{3}{2}x+1$

$y=\frac{3}{2}x-1$

$y=\frac{3}{2}x-5$

Explanation

Rewrite this equation in slope intercept form .

Add on both sides.

The equation becomes:

Divide by two on both sides.

$\frac{2y }{2}= \frac{3x+4}{2}$

The equation in slope intercept form is: $y=\frac{3}{2}x+2$

Shifting this equation down four units means that the y-intercept will be decreased four units.

The answer is: $y=\frac{3}{2}x-2$

6

Shift the graph down four units. What is the new equation?

$y=\frac{3}{2}x-2$

$y=\frac{3}{2}x$

$y=\frac{3}{2}x+1$

$y=\frac{3}{2}x-1$

$y=\frac{3}{2}x-5$

Explanation

Rewrite this equation in slope intercept form .

Add on both sides.

The equation becomes:

Divide by two on both sides.

$\frac{2y }{2}= \frac{3x+4}{2}$

The equation in slope intercept form is: $y=\frac{3}{2}x+2$

Shifting this equation down four units means that the y-intercept will be decreased four units.

The answer is: $y=\frac{3}{2}x-2$

7

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 .

8

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 .

9

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 :

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

10

Which of the following is an equation of a vertical line?

Explanation

Think about the meaning of a vertical line on the coordinate grid. The value changes to any value, yet the value always stays the same. Thus, we are talking about an equation in which the is free, or is not effected, and the is constant. This is an equation of the form , where is a constant.

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