Question

Write the equation of a line that passes ghrough (-2,3) and parrallel to 5x-2y=8

Answer 1

The answer would be y = \frac{5}{2} x + 8

Answer 2

y =
`(5)/(2)` x + 8

Explanation:

the equation of a line in slope- intercept form is

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

rearrange 5x - 2y = 8 into this form

subtract 5x from both sides

- 2y = - 5x + 8 ( divide all terms by - 2 )

y =
`(5)/(2)` x - 4 ← in slope-intercept form

with m =
`(5)/(2)`

• Parallel lines have equal slopes, hence

y =
`(5)/(2)` x + c ← is the partial equation

to find c substitute (- 2, 3) into the partial equation

3 = - 5 + c ⇒ c = 3 + 5 = 8

y =
`(5)/(2)` x + 8 ← equation of parallel line