Question

Please help thanks !

Answer 1

point slope form: y-3=
`-\frac{3}5}`(x+2)

slope-intercept form: y=
`-(3)/(5)`x+
`(9)/(5)`

Explanation:

so to find point-slope form, you first have to find the slope of the line

--slope =
`(y_(2)-y_(1) )/(x_(2) -x_(1) )`=
`(0-3)/(3+2) =-(3)/(5)` (you have to use the two points shown: (-2,3) and (3,0) to plug in for y1, y2, x1, and x2 to find the slope.)

so your slope is
`-(3)/(5)`.

Now all you have to do is use one of the points (-2,3) to sub in for y1 and x1 in the point-slope form equation.

Therefore, you get y-3=
`-(3)/(5)`(x+2) for point-slope form.

Now for slope-intercept form, you already have the slope because you found it to complete the equation for point slope form

slope =
`-(3)/(5)`

Now slope intercept form is y=mx+b, where m is the slope and b is the y-intercept.

So, far we have y=
`-(3)/(5)`x+b

the easiet point to use for the x and y values is (3,0)

so, lets substitute: 0=
`-(3)/(5)`(3)+b, which becomes 0=
`-(9)/(5)`+b

add
`-(9)/(5)` to both sides to get b=
`(9)/(5)`

Now you have both the slope and the y-intercept so you can now write the line in slope-intercept form.

You get
`y=-(3)/(5)x +(9)/(5)`.