The slope of of x – 4y =–4 is 1/4, and the y-intercept is 1. The graph that shows the equation is: D. A coordinate plane with a line passing through (-4, 0) and (0, 1).
Slope (m) = change in y / change in x.
The slope of a line represents m in the slope-intercept form expressed as, y = mx + b.
Given the equation, x - 4y = -4, rewrite in slope-intercept form to determine the slope.
-4y = -x - 4
Divide both sides by -4
y = -x/-4 - 4/-4
y = 1/4x + 1
The slope is 1/4.
The slope between the points (-4, 0) and (0, 1) is: (1 - 0)/(0 - (-4)) = 1/4
The y-intercept of the line is also 1, because y = 1 when x = 0 (0, 1).
Therefore, the answer is: D. A coordinate plane with a line passing through (-4, 0) and (0, 1).
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