Question

a line passes through the point (8, 3) and has a slope of $-\frac{3}{2}$. write an equation in point - slope form for this line.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step2: Identify values of $x_1,y_1$ and $m$

We are given that the line passes through the point $(8,3)$, so $x_1 = 8$ and $y_1=3$. The slope $m=-\frac{3}{2}$.

Step3: Substitute values into the formula

Substitute $x_1 = 8$, $y_1 = 3$ and $m=-\frac{3}{2}$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 3=-\frac{3}{2}(x - 8)$.

Answer:

$y - 3=-\frac{3}{2}(x - 8)$