Question

which of the following sets of points belong to the linear function shown on the coordinate plane?
$(-6, -5)$ and $(2, 3)$
$(-8, 4)$ and $(8, 2)$
$(-12, -7)$ and $(10, 4)$
$(0, -1)$ and $(2, 1)$

Explanation:

Step1: Find line's slope

Identify two points on the graph: e.g., $(2,1)$ and $(0,-1)$.
Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 1}{0 - 2} = \frac{-2}{-2} = 1$

Step2: Find line equation

Use slope-intercept form $y = mx + b$. Substitute $m=1$ and $(2,1)$:
$1 = 1(2) + b$
$b = 1 - 2 = -1$
Equation: $y = x - 1$

Step3: Test Option A points

Test $(-6,-5)$: $-5 = -6 -1 = -7$ → Not true.

Step4: Test Option B points

Test $(-8,4)$: $4 = -8 -1 = -9$ → Not true.

Step5: Test Option C points

Test $(-12,-7)$: $-7 = -12 -1 = -13$ → Not true.

Step6: Test Option D points

Test $(0,-1)$: $-1 = 0 -1 = -1$ → True.
Test $(2,1)$: $1 = 2 -1 = 1$ → True.

Answer:

○ (0, -1) and (2, 1)