Question

How do you write an equation of the line, in point-slope form, that passes through the two given points (-2,15), (9,-18)?

Answer 1

The answer is: `y -15 = (-3) * (x+2)`

The point slope form is:

`y - y_1 = m(x - x_1)`

Source of the Equation

`m` is the slope of the line. So we should find the slope first. Slope is the amount of change in y-axis per the amount of change in x-axis.

`m = (y_2 - y_1)/(x_2 - x_1)`

When we plug our given points to this equation:

`m = (15 - (-18))/(-2-9) -> (-3)`

Now we found the slope of our line. We just need to plug one of the points to the point-slope equation. You can choose any of the given points. Since they are on the same line, final equations will be equivalent.

`y - 15 = (-3) * (x - (-2))`
`y -15 = (-3) * (x+2)`