which graph matches the equation $y + 6=\frac{3}{4}(x + 4)$?

Answer:

The graph with points ((-4,-6)) and ((4,0)) matches the equation.

Explanation:

Step1: Rewrite in slope - intercept form

Starting with (y + 6=\frac{3}{4}(x + 4)), distribute the (\frac{3}{4}): (y+6=\frac{3}{4}x+3). Then subtract 6 from both sides to get (y=\frac{3}{4}x - 3).

Step2: Find the y - intercept

Set (x = 0) in (y=\frac{3}{4}x - 3), then (y=-3).

Step3: Find another point

Set (y = 0) in (y=\frac{3}{4}x - 3), then (0=\frac{3}{4}x - 3), add 3 to both sides: (3=\frac{3}{4}x), multiply both sides by (\frac{4}{3}) to get (x = 4). The line passes through ((0,-3)) and ((4,0)). Also, when (x=-4), (y=\frac{3}{4}(-4)-3=-3 - 3=-6), so it passes through ((-4,-6)) which is shown on the first graph.