Question

What is the slope of the line that passes through
the points (-1,3) and (5, 7)?

Answer 1

`(2)/(3)`

Explanation:

For this situation we will use this equation:

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )`

This lets us find the slope from a set of points (m being the slope of course), with each one representing a coordinate from our set. (e.g. 7 could be
`y_(2)`)

First let's define which coordinates will represent each:

(-1,3):
`x_(1) ,y_(1)`

(5,7):
`x_(2) ,y_(2)`

Now that we have this, we can fill in our coordinates:
`m = (7-3)/(5-(-1))`

Next we simplify:
`m = (4)/(5+1)` (double negative = positive)

And simplify some more:
`m = (4)/(6)`

Finally, we find the GCF (greatest common factor) of 4 and 6, which is 2, and divide by that to further simplify the fraction:
`m = (2)/(3)`

Therefore, the slope of the line that passes through the points (-1,3) and (5,7) is
`(2)/(3)`.