# Lesson 15

Meet Slope

### Problem 1

Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope $$\frac{1}{5}.$$ Label each line with its slope.

### Problem 2

Draw three lines with slope 2, and three lines with slope $$\frac 1 3$$. What do you notice?

### Problem 3

The figure shows two right triangles, each with its longest side on the same line.

1. Explain how you know the two triangles are similar.
2. How long is $$XY$$?
3. For each triangle, calculate (vertical side) $$\div$$ (horizontal side).
4. What is the slope of the line? Explain how you know.

### Problem 4

Triangle $$A$$ has side lengths 3, 4, and 5. Triangle $$B$$ has side lengths 6, 7, and 8.

1. Explain how you know that Triangle $$B$$ is not similar to Triangle $$A$$.

2. Give possible side lengths for Triangle $$B$$ so that it is similar to Triangle $$A$$.

### Solution

(From Unit 2, Lesson 14.)

### Problem 5

Select all the ratios that are equivalent to the ratio $$12:3$$.

A:

$$6:1$$

B:

$$1:4$$

C:

$$4:1$$

D:

$$24:6$$

E:

$$15:6$$

F:

$$1,\!200:300$$

G:

$$112:13$$

### Solution

(From Unit 2, Lesson 3.)

### Problem 6

Triangle $$ABC$$ is a scaled copy of triangle $$DEF$$. Side $$AB$$ measures 12 cm and is the longest side of $$ABC$$. Side $$DE$$ measures 8 cm and is the longest side of $$DEF$$.

1. Triangle $$ABC$$ is a scaled copy of triangle $$DEF$$ with what scale factor?
2. Triangle $$DEF$$ is a scaled copy of triangle $$ABC$$ with what scale factor?