# Lesson 17

Using Equations for Lines

Let’s write equations for lines.

### Problem 1

Select all the points that are on the line through $$(0,5)$$ and $$(2,8)$$.

A:

$$(4,11)$$

B:

$$(5,10)$$

C:

$$(6,14)$$

D:

$$(30,50)$$

E:

$$(40,60)$$

### Problem 2

Here is triangle $$ABC$$.

1. Draw the dilation of triangle $$ABC$$ with center $$(2,0)$$ and scale factor 2.
2. Draw the dilation of triangle $$ABC$$ with center $$(2,0)$$ and scale factor 3.
3. Draw the dilation of triangle $$ABC$$ with center $$(2,0)$$ and scale factor $$\frac 1 2$$.
4. What are the coordinates of the image of point $$C$$ when triangle $$ABC$$ is dilated with center $$(2,0)$$ and scale factor $$s$$?
5. Write an equation for the line containing all possible images of point $$C$$.

### Problem 3

All three points displayed are on the line. Find an equation relating $$x$$ and $$y$$.

### Problem 4

The Empire State Building in New York City is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the Empire State Building on an $$8 \frac{1}{2}$$-inch-by-$$11$$-inch piece of paper. Select a scale that you think is the most appropriate for the scale drawing. Explain your reasoning.

1. 1 inch to 1 foot
2. 1 inch to 100 feet
3. 1 inch to 1 mile
4. 1 centimeter to 1 meter
5. 1 centimeter to 50 meters
6. 1 centimeter to 1 kilometer
(From Unit 2, Lesson 7.)

### Problem 5

Here are some line segments.

1. Which segment is a dilation of $$\overline{BC}$$ using $$A$$ as the center of dilation and a scale factor of $$\frac23$$?
2. Which segment is a dilation of $$\overline{BC}$$ using $$A$$ as the center of dilation and a scale factor of $$\frac32$$?
3. Which segment is not a dilation of $$\overline{BC}$$, and how do you know?