Question

Which i the equation for the line perpendicular to y = -5/3x 34/3 and containing P(-2,3)?

Answer 1

y =
`(3)/(5)`x +
`(21)/(5)`

Explanation:

y = mx + b We need the slope (m) and the y-intercept (b) to write the equation.

Slope:

Perpendicular slopes are the opposite reciprocals. So, our slope (m) is
`(3)/(5)`.

y-intercept:

we will use our slope (m)
`(3)/(5)` plus the value of -2 for x and 3 for y from the point given (-2,3)

y = mx + b

3 =
`(3)/(5)` (-2) + b

3 =
`(-6)/(5)` + b Add
`(6)/(5)` to both sides

3 +
`(6)/(5)` =
`(-6)/(5)` +
`(6)/(5)` + b

`(15)/(5)` +
`(6)/(5)` = b

`(21)/(5)` is the y-intercept or b.

Replace m with
`(3)/(5)` and b with
`(21)/(5)`

y = mx + b

y =
`(3)/(5)` x +
`(21)/(5)`

Helping in the name of Jesus.