Question

Determine the equation of a straight line passing through (-1,3) and parallel to the line whose equation is 3x-5y=10.​

Answer 1

3x - 5y = - 18

Explanation:

the equation of a line in slope- intercept form is

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

given

3x - 5y = 10 ( subtract 3x from both sides )

- 5y = - 3x + 10 ( divide through by - 5 )

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

with slope m =
`(3)/(5)`

• Parallel lines have equal slopes , then

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

to find c substitute (- 1, 3 ) into the partial equation

3 = -
`(3)/(5)` + c ⇒ c = 3 +
`(3)/(5)` =
`(18)/(5)`

y =
`(3)/(5)` x +
`(18)/(5)` ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fractions

5y = 3x + 18 ( subtract 5y from both sides )

0 = 3x - 5y + 18 ( subtract 18 from both sides )

- 18 = 3x - 5y , that is

3x - 5y = - 18 ← in standard form