What is an equation of the line that passes through the point (3,-1)(3,−1) and is parallel to the line 5x+3y=65x+3y=6?

Question

What is an equation of the line that passes through the point (3,-1)(3,−1) and is parallel to the line 5x+3y=65x+3y=6?

Answer 1

Deteremine the slope, m, of 5x + 3y = 6

Use that slope in point-slope form

(y + 1) = m(x - 3)

Answer 2

5x +3y = 6

solve for y= -5x/3 +2

slope is -5/3 = slope of any parallel line

y = -5x/3 + b, to solve for b plug in the given point (3,-1)

-1 = -5(3)/3 + b = -5+b

b = -1+5 = 4

y = -5x/3 +4 is the parallel line through the given point in slope intercept form

or

5x +3y = 12 in standard form