what is the slope of the line that passes through (1,-19) and (-2,-7)

Answer 1

Hi Izzy,

Two points can always be connected by a straight line. That line will have a slope that tells you the line's change in y for every change in x, or its "rise over run." A slope of 2 means that for every 1 step to the right, you take 2 steps up.

To find the slope between two points, find the change in y and divide it by the change in x:

y2 - y1

x2 - x1

We know the coordinates of both points, so make sure to keep them consistent:

Point 1 (x1, y1)

Point 2 (x2, y2)

It doesn't matter which is which of your two points, the math will work out (one way is like multiplying both top and bottom by -1 to get the other way). It is important, however, that your y-coordinates are on top.

y2 - y1 = y1 - y2

x2 - x1 x1 - x2

Plugging the values in:

-19 - (-7) = -12 = -4

1 - (-2) 3

Checking back, that does make sense! Starting at (-2, -7), taking a step to the right and 4 steps down, and repeating twice more, you end up at (1, -19).

Hope this helps! Please reach out with any more questions!