Let's recall the equation to find out the slope of a line:
[tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Next, we substitute our given values into the equation, and simplify:
[tex] \frac{9-7}{6-3}=\frac{2}{3} [/tex]
Now, we insert the slope (2/3) into the y=mx+b equation and substitute the values from one of the coordinates to find what b, the y-intercept is:
[tex] y=\frac{2}{3}x+c \\ 7=\frac{2}{3}(3)+c \\ 7=2+c \\ c=5 [/tex]
So, the y-intercept is 5. We can now put our discovered values for the slope and the y-intercept into one equation:
[tex] y=\frac{2}{3}x+5 [/tex]
The answer is B.
