Lesson 11

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 \(y=2\)

  1. \(y=6x+8\)
  2. \(y=\frac23x\)
  3. \(y=\text-x+5\)
  4. \(y=\frac34x-2\frac12\)
  5. \(y=1.5x +11\)

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: \(y=\frac14 x +\frac54\)

  1. Are \((1,1.5)\) and \((12,4)\) solutions to the equation? Explain or show your reasoning.
  2. 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.
(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. 
A:

Graph A

B:

Graph B

C:

Graph C

D:

Graph D

1:

\(y\) is the weight of a kitten \(x\) days after birth.

2:

\(y\) is the distance left to go in a car ride after \(x\) hours of driving at a constant rate toward its destination.

3:

\(y\) is the temperature, in degrees C, of a gas being warmed in a laboratory experiment.

4:

\(y\) is the amount of calories consumed eating \(x\) crackers.

(From Unit 5, Lesson 8.)