Question

How do you write an equation going through points (-5, 1) (0, -2)?

Answer 1

The standard form of the equation would be
`5y +3x= -10`

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 `(-5,1) and (0,-2)`
`x_1 = -5`
`x_2 = 0`
`y_1 = 1`
`y_2 = -2`

`m = (-2-1)/(0-(-5))`

`m = -3/5`

The slope is `m = -3/5`

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

`m = -3/5`
`x_1 = -5`
`y_1=1`

`y - 1 = -3/5 (x -(-5))`

`y - 1 = -3/5x -3`

`y cancel(-1) cancel(+ 1)= -3/5x -3 +1`

`y = -3/5x -2`

The slope-intercept form of the equation of the line is
`y = -3/5x -2`

`(5)y = (-3/5x -2)(5)`

`5y =-3x-10`

`5y +3x=cancel(-3x) cancel(+3x)-10`

The standard form of the equation would be
`5y +3x= -10`