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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150453Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d218ad76b0ca0b65c67233e5f459571ded875bf04745666694a5b7116d643141)
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150453Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9d2bfee91361ee5a0238cb064e172ee09eda3368da20b55b28d4926f11a0d642)
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150453Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=879c3c08682bc5269dc47a1f3af3d9fdb150f533861aa165fe47deb39ef1ea2e)
- 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 \(A\).