# Lesson 10

Parallel Lines in the Plane

• Let’s investigate parallel lines in the coordinate plane.

### Problem 1

Select all equations that are parallel to the line $$2x + 5y = 8$$.

A:

$$y=\frac{2}{5}x + 4$$

B:

$$y=\text-\frac{2}{5}x + 4$$

C:

$$y-2=\frac{5}{2}(x+1)$$

D:

$$y-2=\text-\frac{2}{5}(x+1)$$

E:

$$10x+5y=40$$

### Problem 2

Prove that $$ABCD$$ is not a parallelogram.

### Problem 3

Write an equation of a line that passes through $$(\text-1,2)$$ and is parallel to a line with $$x$$-intercept $$(3,0)$$ and $$y$$-intercept $$(0,1)$$

### Problem 4

Write an equation of the line with slope $$\frac23$$ that goes through the point $$(\text-2, 5)$$.

(From Unit 6, Lesson 9.)

### Problem 5

Priya and Han each wrote an equation of a line with slope $$\frac13$$ that passes through the point $$(1,2)$$. Priya’s equation is $$y-2 = \frac13 (x-1)$$ and Han’s equation is $$3y - x = 5$$. Do you agree with either of them? Explain or show your reasoning.

(From Unit 6, Lesson 9.)

### Problem 6

Match each equation with another equation whose graph is the same parabola.

(From Unit 6, Lesson 8.)

### Problem 7

A parabola is defined as the set of points the same distance from $$(\text-1, 3)$$ and the line $$y=5$$. Select the point that is on this parabola.

A:

$$(\text-1, 3)$$

B:

$$(0, 5)$$

C:

$$(3,0)$$

D:

$$(0,0)$$

(From Unit 6, Lesson 7.)

### Problem 8

Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.

1. $$(x,y) \rightarrow (2x,y+2)$$
2. $$(x,y) \rightarrow (2x,2y)$$
3. $$(x,y) \rightarrow (x+2,y+2)$$
4. $$(x,y) \rightarrow (x-2,y)$$
(From Unit 6, Lesson 2.)
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