Question

How do you write an equation in slope-intercept form of the line that passes through the points (-7,-3) and (-12,5)?

Answer 1

`y=-8/5x-71/5`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept.

We have to find m and b.

To find m, use the `color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

The 2 points here are (-7 ,-3) and (-12 ,5)

let `(x_1,y_1)=(-7,-3)" and " (x_2,y_2)=(-12,5)`

`rArrm=(5-(-3))/(-12-(-7))=8/(-5)=-8/5`

We can now write the partial equation `y=-8/5x+b`

To find b, substitute either of the 2 given points into the
partial equation

Choosing (-12 ,5) that is x = - 12 and y = 5

`5=(-8/5xx-12)+b`

`rArr5=96/5+brArrb=5-96/5=25/5-96/5=-71/5`

`rArry=-8/5x-71/5" is the equation of the line"`