Question

A linear equation is graphed on the coordinate grid below.





image.png





When graphed on the same coordinate grid, which equation results in a system of equations with exactly one solution?




3
x
+
2
y
=
−
2


x
+
2
y
=
2


6
x
+
4
y
=
8


6
x
+
4
y
=
−
12

Answer 1

x + 2y = 2

Reason: the graphed line has slope −3/2. Converting each choice to slope-intercept form:
- 3x + 2y = −2 → y = −(3/2)x − 1 (slope −3/2)
- x + 2y = 2 → y = −(1/2)x + 1 (slope −1/2)
- 6x + 4y = 8 → y = −(3/2)x + 2 (slope −3/2)
- 6x + 4y = −12 → y = −(3/2)x − 3 (slope −3/2)

Only x + 2y = 2 has a different slope, so it will intersect the given line exactly once.