Question 688483
Parallel lines have the SAME slope.
In y = -7x +5, the slope is -7
(compare to y = mx + b, where m is the slope)
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Perpendicular lines will have the a negative inverse slope of {{{1/7}}}.
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Choose a point on the line y = -7x + 5
pick any x and solve for y
if x = 1
y = -7(1) + 5
y = -7 + 5 = -2
(1, -2)
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Using the point (1, -2) and the slope -7, you can find an equation for a parallel line
y - -2 = -7(x-1)
y + 2 = -7x + 7
y = -7x + 7 - 2
{{{highlight_green(y=-7x+5)}}} ==> equation for a parallel line
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Using the point (1, -2) and the slope of {{{1/7}}}, you can find an equation for a perpendicular line
y - -2 = {{{1/7}}}(x-1)
y + 2 = {{{(1/7)x - 1/7}}}
y = {{{(1/7)x - (1/7)-2}}}
y = {{{(1/7)x - 1/7 - 2(7/7)}}}
y = {{{(1/7)x - 1/7 - 14/7}}}
{{{highlight_green(y=(1/7)x - 15/7)}}} ==> equation for a perpendicular line
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