Question

write the linear equation that gives the rule for this table.
x | y
1 | -3
2 | -1
3 | 1
4 | 3
write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Calculate slope $m$

Choose two points, e.g., $(1, -3)$ and $(2, -1)$.
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-3)}{2 - 1} = \frac{2}{1} = 2$

Step2: Find y-intercept $b$

Use $y = mx + b$, substitute $m=2$, $x=1$, $y=-3$.
$-3 = 2(1) + b$
Solve for $b$: $b = -3 - 2 = -5$

Step3: Form linear equation

Substitute $m=2$ and $b=-5$ into $y = mx + b$.

Answer:

$y = 2x - 5$