Question

write the linear equation that gives the rule for this table.

x | y
5 | -15
6 | -18
7 | -21
8 | -24

write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Find slope (rate of change)

Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-18 - (-15)}{6 - 5} = \frac{-3}{1} = -3$

Step2: Verify slope consistency

Check another pair: $m = \frac{-21 - (-18)}{7 - 6} = \frac{-3}{1} = -3$

Step3: Find y-intercept $b$

Use $y = mx + b$, substitute $x=5, y=-15, m=-3$:
$-15 = (-3)(5) + b$
$-15 = -15 + b$
$b = 0$

Step4: Write linear equation

Substitute $m=-3, b=0$ into $y=mx+b$

Answer:

$y = -3x$