Question

How do you write an equation in slope-intercept form of the line that passes through the points (-2,-1) and (4,2)?

Answer 1

`y=1/2x`

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 points on the line"`

The 2 points here are (-2 ,-1) and (4 ,2)

let `(x_1,y_1)=(-2,-1)" and " (x_2,y_2)=(4,2)`

`rArrm=(2-(-1))/(4-(-2))=3/6=1/2`

We can write the partial equation as `y=1/2x+b`

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

Choosing the point (4 ,2) that is x = 4 and y = 2

`rArr2=(1/2xx4)+b`

`"Thus " 2=2+brArrb=0`

`rArry=1/2x" is the equation of the line"`
graph{1/2x [-10, 10, -5, 5]}