Lesson 13
More Solutions to Linear Equations
Let’s find solutions to more linear equations.
Problem 1
For each equation, find \(y\) when \(x=\text-3\). Then find \(x\) when \(y=2\)
- \(y=6x+8\)
- \(y=\frac23x\)
- \(y=\text-x+5\)
- \(y=\frac34x-2\frac12\)
- \(y=1.5x +11\)
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.
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.
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232225Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=558d61c3256caf34f3dd0211066f046e5da62fdc4babffd8d5398796b5579b14)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232225Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e1d6776d4082d7b9990aa66372ce196dbc87033b334882c360542e8d497b7389)