Question

Equation of the line through (-2,4) and parallel to the line 5x+3y=16​

Answer 1

First, we find the slope of the line 5x+3y=16 by placing it into the slope-intercept form:

5x+3y=16

3y = -5x+16

y = -5/3 x + 16/3

comapring with y =mx + b

We get slope of the line m = -5/3

Now

(x1, y1) = (-2,4)

Equation of the line formula is

y - y1 = m(x-x1)

y - 4 = -5/3[(x - (-2)]

y-4 = -5/3(x+2)

3(y-4)=-5(x+2)

3y-12 = -5x-10

5x + 3y = -10 +12

5x+3y = 2

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