Question

1. this is the graph of the equation $y = -\frac{3}{2}x - 3$.
2. which ordered pairs are solutions to the equation? select all that apply.

$(-2, 0)$
$(2, -6)$
$(0, -3)$
$(-4, 3)$
$(-4, -5)$
$(-6, 6)$

Explanation:

Step1: Test (-2, 0) in equation

Substitute $x=-2, y=0$ into $y=\frac{3}{2}x-3$:
$0=\frac{3}{2}(-2)-3 = -3-3=-6$; $0
eq-6$, not a solution.

Step2: Test (2, -6) in equation

Substitute $x=2, y=-6$ into $y=\frac{3}{2}x-3$:
$-6=\frac{3}{2}(2)-3 = 3-3=0$; $-6
eq0$, not a solution.

Step3: Test (0, -3) in equation

Substitute $x=0, y=-3$ into $y=\frac{3}{2}x-3$:
$-3=\frac{3}{2}(0)-3 = 0-3=-3$; $-3=-3$, is a solution.

Step4: Test (-4, 3) in equation

Substitute $x=-4, y=3$ into $y=\frac{3}{2}x-3$:
$3=\frac{3}{2}(-4)-3 = -6-3=-9$; $3
eq-9$, not a solution.

Step5: Test (-4, -5) in equation

Substitute $x=-4, y=-5$ into $y=\frac{3}{2}x-3$:
$-5=\frac{3}{2}(-4)-3 = -6-3=-9$; $-5
eq-9$, not a solution.

Step6: Test (-6, 6) in equation

Substitute $x=-6, y=6$ into $y=\frac{3}{2}x-3$:
$6=\frac{3}{2}(-6)-3 = -9-3=-12$; $6
eq-12$, not a solution.

Step7: Verify graph points

Check the line: when $x=0$, $y=-3$ (matches the y-intercept on the graph). When $x=-2$, $y=\frac{3}{2}(-2)-3=-6$, so $(-2,-6)$ is a solution (not listed). When $x=2$, $y=\frac{3}{2}(2)-3=0$, so $(2,0)$ is a solution (not listed).

Answer:

(0, -3)