Question
Write the equation of the line that passes through the points and . Put your
answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through points and , we start by calculating the slope using the formula . Plugging in our points, we have:

Now we can use the point-slope form of the line equation, which is . Choosing point :

Simplifying this, we get:

Thus, the equation of the line in point-slope form is:

One interesting fact about lines is that they can be represented in various forms! The slope-intercept form, , is quite popular, as it makes it easy to identify the slope and y-intercept directly.

If you’re ever unsure about your slope calculation, remember that it is just “rise over run”! A common mistake is to switch the coordinates for the slope formula, so double-check that you’re always subtracting in the correct order: over . That small detail makes a big difference!