which point is on the line that passes through (0, 6) and is parallel to the given line?\n○ (-12, 8)\n○ (-6…

Explanation:

Step1: Find slope of given line

Use points $(-12, -2)$ and $(0, -4)$: $\text{slope } m = \frac{-4 - (-2)}{0 - (-12)} = \frac{-2}{12} = -\frac{1}{6}$

Step2: Write target line equation

Parallel lines have equal slope; y-intercept is $(0,6)$: $y = -\frac{1}{6}x + 6$

Step3: Test each option

Option 1: $(-12, 8)$

$y = -\frac{1}{6}(-12) + 6 = 2 + 6 = 8$ (matches)

Option 2: $(-6, 6)$

$y = -\frac{1}{6}(-6) + 6 = 1 + 6 = 7 \neq 6$ (no match)

Option 3: $(2, 8)$

$y = -\frac{1}{6}(2) + 6 = -\frac{1}{3} + 6 \approx 5.67 \neq 8$ (no match)

Option 4: $(6, 0)$

$y = -\frac{1}{6}(6) + 6 = -1 + 6 = 5 \neq 0$ (no match)

Answer:

$(-12, 8)$