Lesson 11
More Solutions to Linear Equations
Problem 1
For each equation, find \(y\) when \(x=\text-3\). Then find \(x\) when \(y=2\)
- \(y=6x+8\)
- \(y=\frac23x\)
- \(y=\text-x+5\)
- \(y=\frac34x-2\frac12\)
- \(y=1.5x +11\)
Solution
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Problem 2
True or false: The points \((6,13)\), \((21,33)\), and \((99,137)\) all lie on the same line. The equation of the line is \(y=\frac43x+5\). Explain or show your reasoning.
Solution
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Problem 3
Here is a linear equation: \(y=\frac14 x +\frac54\)
- Are \((1,1.5)\) and \((12,4)\) solutions to the equation? Explain or show your reasoning.
- Find the \(x\)-intercept of the graph of the equation. Explain or show your reasoning.
Solution
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Problem 4
Find the coordinates of \(B\), \(C\), and \(D\) given that \(AB\) = 5 and \(BC\) = 10.
![line graphed on xy plane with no grid.](https://cms-im.s3.amazonaws.com/PuixhifbbUNZ2sY4UhBatHn6?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T202953Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=480ea34d2266bb8b5bf13e54082d92aef4613b666238ced69e16ef3d70e7be43)
Solution
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(From Unit 2, Lesson 16.)Problem 5
Match each graph of a linear relationship to a situation that most reasonably reflects its context.
![4 graphs of lines labeled A, B, C. D.](https://cms-im.s3.amazonaws.com/hcMavXLtZktkRooPgpYLir8q?response-content-disposition=inline%3B%20filename%3D%228.3.D.PP.Image.03.6.png%22%3B%20filename%2A%3DUTF-8%27%278.3.D.PP.Image.03.6.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T202953Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d3057d50b2e33eb4b92083ad495c93971dd363f0366a199d3794ee5a29a1cc03)
Solution
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(From Unit 5, Lesson 8.)