Answer
The slope of the line running through coordinates (-2, 3) and coordinates (2, 6) is [tex]\frac{3}{4}[/tex]
Explanation
To get the slope of our line, we are going to use the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where
[tex]m[/tex] is the slope of the line
[tex](x_{1},y_{1})[/tex] are the coordinates of the first point on the line
[tex](x_{2},y_{2})[/tex] are the coordinates of the second point
We know that our first point is (-2, 3), so [tex]x_{1}=-2[/tex] and [tex]y_{1}=3[/tex]. We also know that our second point is (2, 6), so [tex]x_{2}=2[/tex] and [tex]y_{2}=6[/tex]. Now let's replace the values in our slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{6-3}{2-(-2)}[/tex]
[tex]m=\frac{3}{2+2}[/tex]
[tex]m=\frac{3}{4}[/tex]
We can conclude that the slope of our line is [tex]\frac{3}{4}[/tex].
