Question

How do you write the equation in slope intercept form given (2,5) and (7,-3)?

Answer 1

The slope-intercept form of the equation of the line is
`y = -8/5x +25/5`

Explanation:

The formula for the slope of a line based upon two coordinate points is

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

For the coordinate points `(2,5) and (7,-3)`
`x_1 = 2`
`x_2 = 7`
`y_1 = 5`
`y_2 = -3`

`m = (-3-5)/(7-2)`

`m = -8/5`

The slope is `m = -8/5`

The point slope formula would be written as
`y - y_1 = m( x - x_1)`

`m = -8/5`
`x_1 = 2`
`y_1=5`

`y - 5 = -8/5 (x -2)`

`y - 5 = -8/5x +16/5`

`y cancel(-5) cancel(+ 5)= -8/5x +16/5 +5`

`y = -8/5x +16/5 +25/5`

The slope-intercept form of the equation of the line is
`y = -8/5x +25/5`

The standard form would be
`5y = -8x +25`