Question

Find an equation of the line passing through the point (-4,6) that is perpendicular to the line y=7/2x+5. Work please.

Answer 1

y =
`-(2)/(7)`x + 4
`(6)/(7)`

Explanation:

We are to find the equation of line 1 which passes through point (-4,6)

Line 1 is perpendicular to line 2.

The equation of line 2 is; y =
`(7)/(2)`x + 5

The slope of line 2 is
`(7)/(2)`

Because the product of two perpendicular line is -1;

The slope of line 1 is -1 ÷
`(7)/(2)` =
`(-2)/(7)`

Taking another point (x,y) on line 1;

Slope = change in y ÷ change in x

`(-2)/(7)` =
`(y - 6)/(x - -4)`

y - 6 =
`(-2)/(7)`(x + 4)

y - 6 =
`(-2)/(7)`x -
`(8)/(7)`

y =
`(-2)/(7)` -
`(8)/(7)` + 6

y =
`-(2)/(7)`x + 4
`(6)/(7)`