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Anarel [89]
3 years ago
6

PLEASE HELP

Mathematics
1 answer:
poizon [28]3 years ago
6 0
Part A
The given line passes through (-2,2) and it is parallel to the line

4x - 3y - 7 = 0


We need to determine the slope of this line by writing it in slope -intercept form.


3y = 4x - 7


y =  \frac{4}{3} x -  \frac{7}{3}
The slope of this line is
\frac{4}{3}


The line parallel to this line also has slope

m =  \frac{4}{3}


The equation is

y =  \frac{4}{3} x + c


We substitute (-2,2)

2 =  \frac{4}{3}( - 2)  + c


c = 2 + \frac{8}{3}  =  \frac{14}{3}


The required equation is


y =  \frac{4}{3} x + \frac{14}{3}


PART B


The given line is


4x - 3y - 7 = 0




The slope of this line is
\frac{4}{3}


The slope of the line perpendicular to it is

m = -  \frac{3}{4}

The equation of the line is

y =  -  \frac{ 3}{4} x + c




We substitute the point, (-2,2)



2=  -  \frac{ 3}{4} ( - 2) + c


2=  \frac{ 3}{2}  + c



c = 2 -  \frac{3}{2}  =  \frac{1}{2}


The equation of the perpendicular line is


y=  -  \frac{ 3}{4} x +  \frac{1}{2}
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