
Nathan B. answered 10/22/21
Elementary and Algebraic skilled
Let's start by putting this in slope-intercept form for ease of use: y = mx + b
x - 4y = 20
-4y = -x + 20
y = 1/4 x - 5
So the slope of the line is 1/4.
Now they want you to form a point-slope equation for a parallel line: y - y1 = m(x - x1)
The slope-intercept formula gave us the point (-5, 0), so to make sure a line is parallel, we can pick a point that has a single coordinate the same, with the other one different. Since we have a slope of 1/4, I'm going to suggest to make the point (4, 0):
y - 0 = 1/4(x - 4)
y = 1/4(x - 4)
And if you distribute, you will get a slope-intercept form, which you can see will have the same slope, but a different 'b', which will make the lines parallel.