15. Which graph matches the linear equation: −2x+3y=-6

Question

(0,4) (1,-10)

(1,2) (0,-4)

(0,2) (1,-1)

(3,0) (0,-2)

Answer 1

To find the matching graph, we can substitute the given points into the equation and see which choice results in a true statement.

Let's try (0,4):
-2(0) + 3(4) = -6
0 + 12 = -6
12 ≠ -6

Let's try (1,-10):
-2(1) + 3(-10) = -6
-2 - 30 = -6
-32 ≠ -6

Let's try (1,2):
-2(1) + 3(2) = -6
-2 + 6 = -6
4 ≠ -6

Let's try (3,0):
-2(3) + 3(0) = -6
-6 + 0 = -6
-6 = -6

None of the points result in a true statement except for (3,0). Thus, the graph that matches the linear equation -2x + 3y = -6 is (3,0)(0,-2).