Question

What is an equation of the line that passes through the point (-5,6) and is parallel to the line 3x+5y=45

Answer 1

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

Explanation:

Change 3x + 5y = 45 to slope intercept form.

`5y = - 3x + 45 \\ (5y)/(5) = ( - 3x)/(5) + (45)/(5) \\ y = ( - 3x)/(5) + 9`

A parallel line has the same slope, therefore, the new equation's slope would be

`( - 3)/(5)`

Using point slope form

`y - y1 = m(x - x1) \\ y - 6 = ( - 3)/(5) (x + 5) \\ y - 6 = ( - 3x)/(5) - 3 \\ y = ( - 3x)/(5) + 3`