Find an equation of the line passing through the point (−6,−5) that is parallel to the line y=4/3x−5

y = x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 5 ← is in slope- intercept form

with slope m =

Parallel lines have equal slopes, thus

y = x + c ← is the partial equation

To find c substitute (- 6, - 5) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = x + 3 ← equation of parallel line

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

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