Use the given conditions to write an equation for the line in standard form.

Question

Passing through (−2,−6) and parallel to the line whose equation is y−1=5/3(x−5).

Write an equation for the line in standard form.

5x - 3y=???

Answer 1

multiply 3 to eliminate fraction: 3[ y-1 = 5/3(x-5)]

3y - 3 = 5(x - 5)

move 3y right and -25 left (change signs) 3y - 3 = 5x - 25

22 = 5x - 3y

Parallel means slope is same and the slope is controlled by the coefficients 5 and -3

Since you have already have the standard form set up ax + by = c, to determine c. substitute in (-2 , -6)

5(-2) - 3(-6) = c

-10 + 18 = c

c = 8 so answer 5x - 3y = 8