Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and

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Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept

Get this in slope-intercept form by adding 5y to each side:
4x - 5y + 5y = 5y + 20

Cancel the 5y's on the left side and we get:
5y + 20 = 4x

Subtract 20 from each side
5y + 20 - 20 = 4x - 20

Cancel the 20's on the left side and we get:
5y = 4x - 20

Divide each side by 5:
5y/5 = 4x/5 - 4
y = 4x/5 - 4

So we have a slope of 4/5

to find our y-intercept, we set x = 0:
y = 4(0)/5 - 4
y = 0 - 4
y = -4

If we want a line perpendicular to the line above, our slope will be the negative reciprocal:
The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator:
m = 5/4

Next, we multiply this by -1:
-5/4

So our slope-intercept of the perpendicular line with the same y-intercept is:
y = -5x/4 - 4