Lesson 12

It’s All on the Line

Problem 1

For each equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither?

1. $$y=0.2x$$
2. $$y=\text- 2x+1$$
3. $$y=5x-3$$
4. $$(y-3)=\text- 5(x-4)$$
5. $$(y-1)=2(x-3)$$
6. $$5x+y=3$$

Solution

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Problem 2

Main Street is parallel to Park Street. Park Street is parallel to Elm Street. Elm is perpendicular to Willow. How does Willow compare to Main?

Solution

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Problem 3

The line which is the graph of $$y=2x-4$$ is transformed by the rule $$(x,y)\rightarrow (\text-x,\text-y)$$. What is the slope of the image?

Solution

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Problem 4

Select all equations whose graphs are lines perpendicular to the graph of $$3x+2y=6$$.

A:

$$3x-2y=4$$

B:

$$2x+3y=6$$

C:

$$2x-3y=8$$

D:

$$(y-4)=\frac23(x-6)$$

E:

$$(y-2)=\text-\frac{3}{2}(x-8)$$

F:

$$y=\frac23x$$

G:

$$y=\frac32x+3$$

Solution

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(From Unit 6, Lesson 11.)

Problem 5

Match each line with a perpendicular line.

Solution

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(From Unit 6, Lesson 11.)

Problem 6

The graph of  $$y = \text{-} 4x + 2$$ is translated by the directed line segment $$AB$$ shown. What is the slope of the image?

Solution

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(From Unit 6, Lesson 10.)

Problem 7

Select all points on the line with a slope of $$\text-\frac{1}2$$ that go through the point $$(4,\text-1)$$.

A:

$$(\text-2, 2)$$

B:

$$(0,2)$$

C:

$$(4, \text-1)$$

D:

$$(0, 1)$$

E:

$$(\text-3, 8)$$

Solution

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(From Unit 6, Lesson 9.)

Problem 8

One way to define a circle is that it is the set of all points that are the same distance from a given center. How does the equation $$(x-h)^2+(y-k)^2=r^2$$ relate to this definition? Draw a diagram if it helps you explain.

Solution

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(From Unit 6, Lesson 4.)