Lesson 15
Meet Slope
Let’s learn about the slope of a line.
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.
 Explain how you know the two triangles are similar.
 How long is \(XY\)?
 For each triangle, calculate (vertical side) \(\div\) (horizontal side).
 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.

Explain how you know that Triangle \(B\) is not similar to Triangle \(A\).
 Give possible side lengths for Triangle \(B\) so that it is similar to Triangle \(A\).
Problem 5
Select all the ratios that are equivalent to the ratio \(12:3\).
\(6:1\)
\(1:4\)
\(4:1\)
\(24:6\)
\(15:6\)
\(1,\!200:300\)
\(112:13\)
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 \(DEF\).
 Triangle \(ABC\) is a scaled copy of triangle \(DEF\) with what scale factor?
 Triangle \(DEF\) is a scaled copy of triangle \(ABC\) with what scale factor?