Question

What is the slope-intercept form of the line passing through `(4, 5)` and `(2, 2)`?

Answer 1

`y = 3/2x - 2`
The equation for slope intercept is `y=mx+b`
For this equation the slope `m = 3/2`
and the y intercept is `b = -2`

Explanation:

The formula for slope is `m =(y_2 - y_1)/(x_2-x_1)`

For the points (4,5) and (2,2) where
`x_1 = 4`
`y_1 =5`
`x_2 = 2`
`y_2 = 2`

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

`m =(2 - 5)/(2-4)`

`m = (-3)/-2`

`m =3/2`

To determine the equation of the line we can use the point slope formula and plug in the values given in the question.

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

`m = 3/2`
`x_1 = 4`
`y_1 = 4`

`(y - 4) = 3/2`(x - 4)#

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

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

`y = 3/2x - 2`

The equation for slope intercept is `y=mx+b`

For this equation the slope `m = 3/2`
and the y intercept is `b = -2`