Question

How do you write the equation of a line through (0,3) and (-2,5)?

Answer 1

`y=-x+3`

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 require 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)" and " (x_2,y_2)" are 2 points on the line"`

The 2 points here are (0 ,3) and (-2 ,5)

let `(x_1,y_1)=(0,3)" and " (x_2,y_2)=(-2,5)`

`rArrm=(5-3)/(-2-0)=2/(-2)=-1`

One of the points here is (0 ,3). That is where the line crosses the y-axis.
Hence the value of b is 3

`rArry=-x+3" is the equation"`