Question

a line passes through the points (10, 10) and (5, 6). what is its equation in point - slope form? use one of the specified points in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(10,10)$ and $(x_2,y_2)=(5,6)$. So $m=\frac{6 - 10}{5 - 10}=\frac{-4}{-5}=\frac{4}{5}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(10,10)$ and $m = \frac{4}{5}$, we get $y-10=\frac{4}{5}(x - 10)$.

Answer:

$y-10=\frac{4}{5}(x - 10)$