Question

How do you write the slope intercept form of a line going through (1,3) and (3,7)?

Answer 1

`y=2x+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 slope and b, the y-intercept.

We require to find m and b.

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

`color(orange)"Reminder " 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 (1 ,3) and (3 ,7)

let `(x_1,y_1)=(1,3)" and " (x_2,y_2)=(3,7)`

`rArrm=(7-3)/(3-1)=4/2=2`

We can now write the partial equation as y = 2x + b

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

Using (1 ,3) that is x = 1 and y = 3

`3=(2xx1)+brArr3=2+brArrb=1`

`rArry=2x+1" is the equation in slope-intercept form"`