Question

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

Answer 1

$\huge\boxed{y=-\frac{4}{13}+1}$

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

$\begin{aligned}m&=\frac{y_2-y_1}{x_2-x_1}\\&=\frac{-3-1}{13-0}\\&=\frac{-4}{13}\\&=-\frac{4}{13}\end{aligned}$

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

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

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

$\begin{aligned}y-1&=-\frac{4}{13}x\\y&=-\frac{4}{13}x+1\end{aligned}$