Question

PLease answer this correctly?

Answer 1

`y+4=-(1)/(2) (x-5)`

This is the equation of the line perpendicular to the equation line through the points given that crosses through (-4,5)

Explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and can find the slope.

Point slope:
`y-y_1=m(x-x_1)`

We must find the slope using the graph. We pick two points which intersect with grid lines from the line given.

Slope:
`m=(y_2-y_1)/(x_2-x_1)`

We substitute
`x_1=3\\y_1=2` and
`x_2=2\\y_2=0`

`m=(0-2)/(2-3)`

`m=(-2)/(-1)=(2)/(1) =2`

`m\\eq 2` in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is
`m=-(1)/(2)`.

We will substitute
`m=-(1)/(2)` and now use the point they gave us (-4,5)
`x_1=-4\\y_1=5`.

`y-(-4)=-(1)/(2) (x-5)`

`y+4=-(1)/(2) (x-5)`

This is the equation of the line perpendicular to the equation line through the points given that crosses through (-4,5)