Answer:
[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
For this situation we have the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where each variable represents a coordinate (e.g. in this case 4 could be [tex]y_{1}[/tex]). So first, let's define which coordinates will be the values of these variables:
(3,4): [tex]x_{1}, y_{1}[/tex]
(5,9): [tex]x_{2}, y_{2}[/tex]
Now we need to replace each variable with its given value: [tex]m = \frac{9-4}{5-3}[/tex]
And then do the subtraction to simplify: [tex]m=\frac{5}{2}[/tex]
Therefore, the slope of the line that passes through the points (3,4) and (5,9) is [tex]\frac{5}{2}[/tex].
