Question

A line passes through the points (0,1) and (13,-3). What is it’s equation in slope intercept form.

Answer 1

`\huge\boxed{y=-(4)/(13)+1}`

First, let's find the slope (
`m`) of the line using the two points:

`\begin{aligned}m&=(y_2-y_1)/(x_2-x_1)\\&=(-3-1)/(13-0)\\&=(-4)/(13)\\&=-(4)/(13)\end{aligned}`

Now, we'll use point-slope form using the first point and the slope to get an equation for the line.

`\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=-(4)/(13)(x-0)\end{aligned}`

Now, we just need to get the equation to slope-intercept form, which is
`y=mx+b`.

`\begin{aligned}y-1&=-(4)/(13)x\\y&=-(4)/(13)x+1\end{aligned}`