Answer:
(-6, 9), (-5, 13)
(-8.25, 0), (0, 33)
Step-by-step explanation:
You want some points on the line given by y -9 = 4(x +6).
Point-slope form
The point-slope equation of a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Comparing this form to the given equation, we see ...
m = 4, (h, k) = (-6, 9)
One of the points on the line with slope 4 is (-6, 9).
Slope
The slope of the line is the ratio "rise"/"run". The slope of 4 means the line goes up 4 units for each unit to the right. One unit right of x=-6 is x=-5. Four units up from y=9 is y=13. So, using the value of slope, we find another point on the line is (-5, 13).
Two points on the line are (-6, 9) and (-5, 13).
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Additional comment
There are infinitely many points that would fall on this line. The two given here are sufficient for you to graph the line. If you need to identify others, you can plot your answer choices and see which ones fall on the graph. Or, you can try the (x, y) values in the equation to see which ones satisfy it.
The intercepts of this line are (-8.25, 0) and (0, 33).
