Question

Answer please cuz I'm very confused

Answer 1

5x + 3y = - 53

the equation of a line in ' slope- intercept form ' is y = mx + c

where m is the slope and c the y-intercept

rearrange 3x - 5y = - 15 into this form to obtain m → (subtract 3x from both sides)

- 5y = - 3x - 15 → divide all terms by - 5 )

y =
`(3)/(5)` x + 3 → in slope-intercept form with m =
`(3)/(5)`

given a line with slope m then the slope m₁ of a line perpendicular to it is

m₁ = -
`(1)/(m)` = - 1 ÷
`(3)/(5)` = -
`(5)/(3)`

partial equation is y = -
`(5)/(3)` x + c

to find c substitute ( - 7, - 6) into the partial equation

- 6 =
`(35)/(3)` + c ⇒ c = - 6 -
`(35)/(3)` = -
`(53)/(3)`

y = -
`(5)/(3)` x -
`(53)/(3)` → in slope intercept form

multiply all terms by 3

3y = - 5x - 53 → ( add 5x to both sides )

5x + 3y = - 53 → in standard form