First we need to find slope of given line −4x+3y=−2
So convert it into slope intercept form y=mx+b
−4x+3y=−2
3y=4x−2
y=4/3x−2/3
Comparing above equation with y=mx+b gives m=4/3
Hence slope of given line is 4/3.
We need slope of perpendicular line which is always "negative reciprocal of given slope".
Negative of 4/3 is -4/3.
taking reciprocal gives -3/4
Hence slope of required perpendicular line is m=-3/4
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Now we need to find y-intercept of −7x−7y=6
y-intercept is always the y-value when x=0 so let's plug x=0 into −7x−7y=6
−7(0)−7y=6
0−7y=6
−7y=6
y=-6/7
y-intercept is also called "b" in y=mx+b
hence b=-6/7
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Now we know that slope of perpendicular line is m=-3/4 and y-intercept b=-6/7
so plug both into formula y=mx+b
We get Final answer is
