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Explanation:
Pick any number you want for x. I find x = 0 to be easiest. Plug this into the equation to get...
y = -4x-4
y = -4(0) - 4
y = 0-4
y = -4
This is the y intercept. The graph crosses the y axis at -4. So one point on this line is (0,-4) since x = 0 and y = -4 pair up together
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Repeat for another x value, say x = 1
y = -4x-4
y = -4(1)-4
y = -4-4
y = -8
We have x = 1 and y = -8 pair up now. Therefore another point on this line is (1,-8)
We could repeat for other x values, but we have enough info to graph this straight line. We only need two points minimum to graph a straight line.
So from here all you need to do is plot (0,-4) and (1,-8). Then draw a straight line through the two points. The line extends infinitely out in both directions.
You could use any other two points you wanted. For me I just find it easiest to work with 0 and anything close to it.
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Note how starting at (0,-4) we have moved 4 units down and 1 unit to the right to arrive at (1,-8). The "4 units down, 1 unit to the right" comes exactly from the slope of -4 = -4/1
slope = rise/run = -4/1
rise = -4 means we move down 4
run = 1 means we move 1 to the right
