Question

a line passes through the points (-3, -2) and (7, 3). 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, $(x_1,y_1)=(-3,-2)$ and $(x_2,y_2)=(7,3)$. So $m=\frac{3-(-2)}{7-(-3)}=\frac{3 + 2}{7+3}=\frac{5}{10}=\frac{1}{2}$.

Step2: Write the point - slope form

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

Answer:

$y + 2=\frac{1}{2}(x + 3)$