Question

(15,-4); 7x-3y=-5

Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in​ slope-intercept form, if possible.

Answer 1

y =
`(7)/(3)` x - 39

Explanation:

the equation of a line in slope- intercept form is

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

given the line with equation

7x - 3y = - 5 ( subtract 7x from both sides )

- 3y = - 7x - 5 ( multiply through by - 1 )

3y = 7x + 5 ( divide through by 3 )

`(3)/(3)` y =
`(7)/(3)` x +
`(5)/(3)` ← in slope- intercept form

with slope m =
`(7)/(3)`

• Parallel lines have equal slopes , then

y =
`(7)/(3)` x + c ← is the partial equation of the parallel line

to find c, substitute the point (15, - 4 ) for x and y into the partial equation

- 4 =
`(7)/(3)` (15) + c = 35 + c ( subtract 35 from both sides )

- 39 = c

y =
`(7)/(3)` x - 39 ← equation of parallel line