Question

(slope-intercept form mc)
the table shown represents a linear relationship.

x 0 1 2 3
y -6 -4 -2 0

based on the table, what is the equation of the linear relationship in slope-intercept form?
○ a $y=2x+6$
○ b $y=2x-6$
○ c $y=-2x+3$
○ d $y=-2x-3$

Explanation:

Step1: Identify y-intercept (b)

When $x=0$, $y=-6$, so $b=-6$.

Step2: Calculate slope (m)

Use two points, e.g., $(0,-6)$ and $(1,-4)$.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-(-6)}{1-0}=\frac{2}{1}=2$

Step3: Write slope-intercept equation

Slope-intercept form is $y=mx+b$. Substitute $m=2$, $b=-6$.
$y=2x-6$

Step4: Verify with table values

For $x=2$: $y=2(2)-6=-2$ (matches table). For $x=3$: $y=2(3)-6=0$ (matches table).

Answer:

b. $y=2x-6$