Question

Identify an equation in point-slope form for the line parallel to y=-(2)/(3)x+8 that passes through (4,-5)

Answer 1

Parallel lines have same slopes.

Given,

Our required line equation is parallel to

y = -2x/3 + 8

So slope of our required line is -2/3

Equation of a line passing through the point (x1,y1) and having slope m is

y - y1 = m(x - x1)

Here point is (4,-5) and slope is -2/3

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

3y - 12 = - 2x - 10

3y = - 2x + 2

2x + 3y = 2 is the required equation.