Question

How do you write an equation given points (1,2), (3,8)?

Answer 1

`y=3x-1`

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

The 2 points here are (1 ,2) and (3 ,8)

let `(x_1,y_1)=(1,2)" and " (x_2,y_2)=(3,8)`

`rArrm=(8-2)/(3-1)=6/2=3`

We can write the partial equation as y = 3x + b

To find b, substitute either of the 2 given points into the
partial equation and solve for b.

Using (1 ,2), that is x = 1 and y = 2.

`2=(3xx1)+brArr2=3+brArrb=-1`

`rArry=3x-1" is the equation"`