# 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 \(ABC\).

- Draw the dilation of triangle \(ABC\) with center \((2,0)\) and scale factor 2.
- Draw the dilation of triangle \(ABC\) with center \((2,0)\) and scale factor 3.
- Draw the dilation of triangle \(ABC\) with center \((2,0)\) and scale factor \(\frac 1 2\).
- What are the coordinates of the image of point \(C\) when triangle \(ABC\) is dilated with center \((2,0)\) and scale factor \(s\)?
- 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 inch to 1 foot
- 1 inch to 100 feet
- 1 inch to 1 mile
- 1 centimeter to 1 meter
- 1 centimeter to 50 meters
- 1 centimeter to 1 kilometer

### Problem 5

Here are some line segments.

- Which segment is a dilation of \(\overline{BC}\) using \(A\) as the center of dilation and a scale factor of \(\frac23\)?
- Which segment is a dilation of \(\overline{BC}\) using \(A\) as the center of dilation and a scale factor of \(\frac32\)?
- Which segment is not a dilation of \(\overline{BC}\), and how do you know?