Example

A line with $y$-intercept $(0,2)$ passes through the other point $(1,9)$. Find the point-slope form of the equation for the line. Also write the equation is standard form.

Solution

We are given the $y$-intercept, but we don't have the slope. Our first task is to compute slope:

Now we have

so that the slope-intercept form is

We can determine standard form by getting both variables on the left: