Lesson 10
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.
![Three lines on a grid. The black line begins at 0 comma 5 & rises 1 vertical unit for each 5 horizontal units. The yellow line at 0 comma 3, the blue line begins at 0 comma 8. They meet at 5 comma 13.](https://cms-im.s3.amazonaws.com/wQTyTM9xkYqMwzxHDuyaaojA?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003324Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ead3e921c191684aae40576d9ead6757e90a3b111081ccbcd2c64d2f717b6a80)
Problem 2
Draw three lines with slope 2, and three lines with slope \(\frac 1 3\). What do you notice?
![Blank grid, 14 blocks wide, 11 blocks high.](https://cms-im.s3.amazonaws.com/WDhBYXN31LAEAvFTFJquQdVU?response-content-disposition=inline%3B%20filename%3D%228-8.2.10.Image.Revision.109.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.10.Image.Revision.109.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003324Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9ae2a9ac872491511f40f42f0e2c37714dd56907e884291a0b3b9a9d8ccda630)
Problem 3
The figure shows two right triangles, each with its longest side on the same line.
![Two triangles. First horizontal side length 4, vertical side length 2, Second horizontal side length 6, vertical side length 3.](https://cms-im.s3.amazonaws.com/Siuj9VC3oYZt4Rz5bkbUbNms?response-content-disposition=inline%3B%20filename%3D%228-8.2.C10.newPP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C10.newPP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003324Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7011e6ca3049ceb287c0f7a9cbe6f92b3ed78408e4c45b12c2a9ce83ce5cfdf2)
- 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.
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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 \(A\).