Question

What is the slope-intercept form of the line passing through `(5, 1)` and `0, -6)`?

Answer 1

`y=7/5x-6`

Explanation:

Recall that the general formula for a line in slope-intercept form is:

`color(blue)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))`

where:
`y=`y-coordinate
`m=`slope
`x=`x-coordinate
`b=`y-intercept

Determining the Equation of the Line
`1`. Start by determining the slope between the two points using the slope formula. When determining the slope, either `(5,1)` or `(0,-6)` can be coordinate `1` or `2`.

As long as you do the calculations correctly, it doesn't matter which one you choose. In this case, we will let coordinate `1` be `(5,1)` and coordinate `2` be `(0,-6)`.

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

`m=(-6-1)/(0-5)`

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

`m=7/5`

`2`. Substitute `m=7/5` into `y=mx+b`. Choose either coordinate `1` or `2` into substitute into the equation. In this case, we will choose coordinate `1`. Then solve for `b`.

`y=7/5x+b`

`1=7/5(5)+b`

`1=7+b`

`b=-6`

`3`. Write out the equation.

`color(green)(|bar(ul(color(white)(a/a)y=7/5x-6color(white)(a/a)|)))`