Question

write the equation in point slope form using either point.

Explanation:

Step1: Calculate the slope

The slope $m$ formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(6,5)$. So $m=\frac{5 - 3}{6 - 1}=\frac{2}{5}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(1,3)$ and $m = \frac{2}{5}$, we get $y - 3=\frac{2}{5}(x - 1)$. Using the point $(6,5)$ and $m=\frac{2}{5}$, we get $y - 5=\frac{2}{5}(x - 6)$.

Answer:

$y - 3=\frac{2}{5}(x - 1)$ or $y - 5=\frac{2}{5}(x - 6)$