Question

What is the equation of the line, in slope-intercept form, that passes through (3,-1) and (-1, 5)?

2 x + 3 y - 7 = 0
2 y=-3x+7
ASAP PLEASE

Answer 1

`2y = -3x+7`

Explanation:

The coordinates are (3,-1) and (-1,5)

Finding the slope :

Slope =
`(rise)/(run)`

Slope =
`(5+1)/(-1-3)`

Slope =
`(6)/(-4)`

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

Now Finding y-intercept.

For this, we'll take any point

Let it be (3,-1)

So,

Point = (x,y) = (3,-1)

=> x = 3, y = -1

Putting in slope intercept form to get b

=>
`y = mx+b`

=> -1 = (3)(
`-(3)/(2)`) + b

=> b = -1 +
`(9)/(2)`

=> b =
`(7)/(2)`

Putting m and b in the slope intercept form to get the required equation of line

=>
`y = mx+b`

=>
`y = (-3x+7)/(2)`

=>
`2y = -3x+7`