Question

x -8 -6 -4 -2 0
y 12 6 0 -6 -12
write the equation that created this table.
y = 6x + 12
y = -3x - 12
y = 6x - 12
y = -6x - 4

Explanation:

Step1: Identify y-intercept

From the table, when $x=0$, $y=-12$. So the y-intercept $b=-12$.

Step2: Calculate slope m

Use two points, e.g., $(0, -12)$ and $(-2, -6)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-6 - (-12)}{-2 - 0}=\frac{6}{-2}=-3$

Step3: Form linear equation

Linear form: $y=mx+b$
Substitute $m=-3$, $b=-12$: $y=-3x-12$

Step4: Verify with other points

Test $x=-4$: $y=-3(-4)-12=12-12=0$, matches the table.
Test $x=-6$: $y=-3(-6)-12=18-12=6$, matches the table.
Test $x=-8$: $y=-3(-8)-12=24-12=12$, matches the table.

Answer:

y = -3x - 12