Question

How do you write the equation in slope intercept form given (2, 2), (-1, 4)?

Answer 1

The slope-intercept form of the equation is `y=-2/3x+10/3`

Explanation:

The slope-intercept form of the equation of the line is `y=mx+b`
where `m=` slope and `b=` the y intercept

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

`x_1=2`
`y_1=2`
`x_2=-1`
`y_2=4`

`m = (4-2)/(-1-2)`

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

`m=-2/3`

Now use the point slope formula to solve for the equation of the line.

`(y-y_1)=m(x-x_1)`

For this situation we are given the slope of `3` and a point of `(2,1)`

`m=-2/3`
`x_1=2`
`y_1=2`

`(y-y_1)=m(x-x_1)`

`(y-2)=-2/3(x-2)`

`y-2=-2/3x-4/3`

`y cancel(-2) cancel(+2)=-2/3x+4/3 + 2`

`y=-2/3x+4/3 +6/3`

`y=-2/3x+10/3`

Answer 2

`y = (-2x)/3 +10/3`

Explanation:

If you have two points on a straight line, there is a lovely formula which allows you to get the equation immediately. It is based on the formula for the slope, so you kill two birds with one stone!

`(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)`

`(y-2)/(x-2) = (4-2)/(-1-2) = 2/-3 " this value is the slope"`

`(y-2)/(x-2) = -2/3" cross multiply"`

`3y - 6 = -2x +4`

`3y = -2x +10`

`y = (-2x)/3 +10/3`