4.1 Use the Rectangular Coordinate System

Before you get started, take this readiness quiz.

Evaluate $x + 3$ when $x = −1$.
If you missed this problem, review the reference.

Evaluate $2 x - 5 y$ when $x = 3$ and $y = −2 .$
If you missed this problem, review the reference.

Solve for $y$: $40 - 4 y = 20$.
If you missed this problem, review the reference.

Which of the following ordered pairs are solutions to $2 x + 3 y = 6$?

ⓐ $\left(3 , 0\right)$ ⓑ $\left(2 , 0\right)$ ⓒ $\left(6 , −2\right)$

Which of the following ordered pairs are solutions to the equation $4 x - y = 8$?

ⓐ $\left(0 , 8\right)$ ⓑ $\left(2 , 0\right)$ ⓒ $\left(1 , −4\right)$

Which of the following ordered pairs are solutions to the equation $y = 4 x - 3$?

ⓐ $\left(0 , 3\right)$ ⓑ $\left(1 , 1\right)$ ⓒ $\left(−1 , −1\right)$

Which of the following ordered pairs are solutions to the equation $y = −2 x + 6$?

ⓐ $\left(0 , 6\right)$ ⓑ $\left(1 , 4\right)$ ⓒ $\left(−2 , −2\right)$

Complete the table to find three solutions to this equation: $y = 3 x - 1$.

Complete the table to find three solutions to this equation: $y = 6 x + 1$.

Complete the table to find three solutions to this equation: $2 x - 5 y = 20$.

Complete the table to find three solutions to this equation: $3 x - 4 y = 12$.

Find three solutions to this equation: $y = −2 x + 3$.

Find three solutions to this equation: $y = −4 x + 1$.

Find three solutions to the equation $2 x + 3 y = 6$.

Find three solutions to the equation $4 x + 2 y = 8$.

Which ordered pairs are solutions to the given equations?

$2 x + y = 6$

1. ⓐ $\left(1 , 4\right)$
2. ⓑ $\left(3 , 0\right)$
3. ⓒ $\left(2 , 3\right)$

Which ordered pairs are solutions to the given equations?

$4 x - 2 y = 8$

1. ⓐ $\left(3 , 2\right)$
2. ⓑ $\left(1 , 4\right)$
3. ⓒ $\left(0 , −4\right)$

Which ordered pairs are solutions to the given equations?

$y = 4 x + 3$

1. ⓐ $\left(4 , 3\right)$
2. ⓑ $\left(−1 , −1\right)$
3. ⓒ $\left(\frac{1}{2} , 5\right)$

Which ordered pairs are solutions to the given equations?

$y = \frac{1}{2} x - 1$

1. ⓐ $\left(2 , 0\right)$
2. ⓑ $\left(−6 , −4\right)$
3. ⓒ $\left(−4 , −1\right)$

Complete the table to find solutions to each linear equation.

$y = 2 x - 4$

Complete the table to find solutions to each linear equation.

$y = − x + 5$

Complete the table to find solutions to each linear equation.

$y = \frac{1}{3} x + 1$

Complete the table to find solutions to each linear equation.

$y = - \frac{3}{2} x - 2$

Complete the table to find solutions to each linear equation.

$x + 3 y = 6$

Complete the table to find solutions to each linear equation.

$2 x - 5 y = 10$

Find three solutions to each linear equation.

$y = 5 x - 8$

Find three solutions to each linear equation.

$y = −4 x + 5$

Find three solutions to each linear equation.

$x + y = 8$

Find three solutions to each linear equation.

$x + y = −2$

Find three solutions to each linear equation.

$3 x + y = 5$

Find three solutions to each linear equation.

$4 x - y = 8$

Find three solutions to each linear equation.

$2 x + 4 y = 8$

Find three solutions to each linear equation.

$5 x - 2 y = 10$

Explain in words how you plot the point $\left(4 , −2\right)$ in a rectangular coordinate system.

Is the point $\left(−3 , 0\right)$ on the x-axis or y-axis? How do you know?