Example

Find an equation of the line passing through the points $(1,4)$ and $(-3,7)$. Write your final answer in standard form.

Solution

Since we are not given the slope of the line, we start by finding it:

Now we can use the slope along with either one of the given points to write the point-slope form equation. Let's use $(x_0,y_0)=(1,4)$ to get

We must write our final answer in standard form...

Although it is not necessary, we could multiply both sides by 4 to clear fractions: