Question

Write an equation for a line that passess through the point (8,5)?

Answer 1

There are infinitely many lines that pass through that point (one example: `y = x-3`).

Check out this interactive graph for an idea of what this would look like.

Explanation:

There are infinitely many lines that could pass through a given point. For example, consider the diagram below:


All of those lines pass through the point `(0, 0)`.

Why? Well, let's set up a point-slope equation for a line going through `(8,5)`:

`y = m(x-8)+5`

For each different value of `m` you plug in, you will get a different equation for your line.

To get a better idea of how this works, check out this interactive graph I created. Slide the slider to pick random values for `m`, and see how your line changes!

Hope that helps :)