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find the equation of the lines parallel to 5x + 4y -20=0 and passing at distance + and - from the point (5,7). show your complete solution

Sagot :

Parallel lines have the same slope.

Change 5x + 4y - 20 = 0  to  y=mx + b:
5x + 4y - 20 =0
4y = -5x + 20
4y/4 = -5x/4 + 20/4
y = -5x/4 + 5

m (slope) = -5/4

Use the slope -5/4 to find the other equation given the points (5,7).
m = -5/4   Point = (5,7)

Slope-Point Form:
[tex]y - y _{1} = m(x - x_{1} )[/tex]
y - 7 = -5/4 (x - 5)
y  = -5x/4 + 25/4 + 7

LCD: 4
(4)y = (4) -5x/4 + (4) 25/4 + (4) 7
4y = -5x + 25 + 28
4y = -5x + 53
5x + 4y - 53 = 0

ANSWER:  5x + 4y - 53 = 0