Question

the table below shows a linear relations. write the equation for this relationship in the slope intercept form, $y = mx + b$.

$x$	$-6$	$-3$	$0$	$9$	$12$
$y$	$2$	$3$	$4$	$7$	$8$

• $y = -9x + 4$
• $y = \frac{1}{3}x + 4$
• $y = \frac{1}{3}x - 3$
• $y = 3x + 4$

Explanation:

Step1: Identify y-intercept ($b$)

When $x=0$, $y=4$, so $b=4$.

Step2: Calculate slope ($m$)

Use two points, e.g., $(0,4)$ and $(3,3)$:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-4}{-3-0}=\frac{-1}{-3}=\frac{1}{3}$

Step3: Build slope-intercept equation

Substitute $m=\frac{1}{3}$ and $b=4$ into $y=mx+b$:
$y=\frac{1}{3}x+4$

Step4: Verify with other points

Test $x=9$: $y=\frac{1}{3}(9)+4=3+4=7$, which matches the table.

Answer:

$\boldsymbol{y=\frac{1}{3}x+4}$ (Option B)