Question

Given the two ordered pairs (1,-2), and (3,-8), how do you write the equation of then line in slope intercept form?

Answer 1

`y = -3x+1`

Explanation:

The slope for a line passing through `(1,-2)` and `(3,-8)` is
`color(white)("XXXX")` `m = (Delta y)/(Delta x) = ((-8)-(-2))/(3-1) = -3`

For a general point `(x,y)` on this line the slope is
`color(white)("XXXX")` `(y-(-2))/(x-1)`

Since the slope is constant for a straight line
`color(white)("XXXX")` `(y+2)/(x-1) = -3`
`rArr`
`color(white)("XXXX")` `y+2= -3x+3`
`rArr`
`color(white)("XXXX")` `y = -3x+1`
`color(white)("XXXX")` `color(white)("XXXX")`which is the slope-intercept form
`color(white)("XXXX")` `color(white)("XXXX")`with slope `(-3)`
`color(white)("XXXX")` `color(white)("XXXX")`and y-intercept `1`