The equation for the line passing through (-8,8) and parallel to the line whose equation is 5x-8y-7=0 is 8y - 5x - 104 = 0
The parallel equation is given as:
5x - 8y - 7 = 0
Add 7 to both sides of the equations
5x - 8y = 7
Rewrite the equation as:
8y = 5x - 7
Divide through the equation by 8
y = 5x/8 - 7/8
The slope of the above equation is 5/8
Parallel lines have equal slope
So, we have
m = 5/8
The equation is then calculated as:
y = m(x - x1) + y1
Where
(x1, y1) = (-8, 8)
So, we have:
y = 5/8(x + 8) + 8
Multiply through by 8
8y = 5(x + 8) + 64
Expand the bracket
8y = 5x + 104
This gives
8y - 5x - 104 = 0
Hence, the equation for the line passing through (-8,8) and parallel to the line whose equation is 5x-8y-7=0 is 8y - 5x - 104 = 0
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