Lesson 9

Equations of Lines

Problem 1

Select all the equations that represent the graph shown.

A:

$$3x-2y=6$$

B:

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

C:

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

D:

$$y-3=\frac{3}{2}(x-4)$$

E:

$$y-6=\frac{3}{2}(x-2)$$

Problem 2

A line with slope $$\frac32$$ passes through the point $$(1,3)$$.

1. Explain why $$(3,6)$$ is on this line.
2. Explain why $$(0,0)$$ is not on this line.
3. Is the point $$(13,22)$$ on this line? Explain why or why not.

Problem 3

Write an equation of the line that passes through $$(1,3)$$ and has a slope of $$\frac{5}{4}$$.

Problem 4

A parabola has focus $$(3,\text{-}2)$$ and directrix $$y=2$$. The point $$(a,\text{-}8)$$ is on the parabola. How far is this point from the focus?

A:

6 units

B:

8 units

C:

10 units

D:

cannot be determined

Solution

(From Unit 6, Lesson 8.)

Problem 5

Write an equation for a parabola with each given focus and directrix.

1. focus: $$(5, 2)$$; directrix: $$x$$-axis
2. focus: $$(\text{-}2, 3)$$; directrix: the line $$y=7$$
3. focus: $$(0,7)$$; directrix: $$x$$-axis
4. focus: $$(\text{-}3, \text- 4)$$; directrix: the line $$y=\text-1$$

Solution

(From Unit 6, Lesson 8.)

Problem 6

A parabola has focus $$(\text{-}1,6)$$ and directrix $$y=4$$. Determine whether each point on the list is on this parabola. Explain your reasoning.

1. $$(\text{-}1,5)$$
2. $$(1 ,7)$$
3. $$(3, 9)$$

Solution

(From Unit 6, Lesson 7.)

Problem 7

Select the center of the circle represented by the equation $$x^2 + y^2 - 8x + 11y - 2 = 0$$.

A:

$$(8, 11)$$

B:

$$(4, 5.5)$$

C:

$$(\text-4, \text-5.5)$$

D:

$$(4, \text-5.5)$$

Solution

(From Unit 6, Lesson 6.)

Problem 8

Reflect triangle $$ABC$$ over the line $$x=\text-6$$.

Translate the image by the directed line segment from $$(0,0)$$ to $$(5,\text-1)$$.

What are the coordinates of the vertices in the final image?