Question

How do you find an equation of the line passing through the given points (-4,-7) and (-8, -8)?

Answer 1

`y=1/4x-6`

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.

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)" and " (x_2,y_2)" are 2 coordinate points"`

here the 2 points are `(-4 ,-7) and (-8 ,-8)`

let `(x_1,y_1)=(-4,-7)" and " (x_2,y_2)=(-8,-8)`

`rArrm=(-8-(-7))/(-8-(-4))=(-1)/(-4)=1/4`

We can now write the partial equation as.

`y=1/4x+b`

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

Using (-4 ,-7). That is `x= - 4 and y = - 7`

`(1/4xx-4)+b=-7rArr-1+b=-7rArrb=-6`

`rArry=1/4x-6" is the equation"`