Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
For this situation we will use this equation:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
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 [tex]y_{2}[/tex])
First let's define which coordinates will represent each:
(-1,3): [tex]x_{1} ,y_{1}[/tex]
(5,7): [tex]x_{2} ,y_{2}[/tex]
Now that we have this, we can fill in our coordinates: [tex]m = \frac{7-3}{5-(-1)}[/tex]
Next we simplify: [tex]m = \frac{4}{5+1}[/tex] (double negative = positive)
And simplify some more: [tex]m = \frac{4}{6}[/tex]
Finally, we find the GCF (greatest common factor) of 4 and 6, which is 2, and divide by that to further simplify the fraction: [tex]m = \frac{2}{3}[/tex]
Therefore, the slope of the line that passes through the points (-1,3) and (5,7) is [tex]\frac{2}{3}[/tex].
