Question

Find the equation of the line that passes through the point (−3, −4) and is parallel to the line that passes through the points (−5, 1) and (7, −3).

Answer 1

`y = -(1)/(3)x - 5`

Explanation:

To write the equation of a line use the point slope formula
`y - y_1 = m(x-x_1)`. Find m by using the slope formula with the points.

`m = (y_2-y_1)/(x_2-x_1) = (1--3)/(-5-7) =(4)/(-12) =-(1)/(3)`

Since the line is parallel, it will have the same slope.

Substitute m = -1/3 and (-3,-4).

`y --4 = -(1)/(3)(x --3)\\y + 4 = -(1)/(3)(x+3)\\y +4 = -(1)/(3)x - 1\\y = -(1)/(3)x - 5`