Question

a line has a slope of \\(\frac{5}{2}\\) and passes through the point (8, 5). what is its equation in point - slope form? use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Recall point - slope formula

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

Step2: Identify values of m, x₁, y₁

We are given that the slope $m = \frac{5}{2}$ and the point $(x_1,y_1)=(8,5)$.

Step3: Substitute values into formula

Substitute $m=\frac{5}{2}$, $x_1 = 8$ and $y_1=5$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y - 5=\frac{5}{2}(x - 8)$.

Answer:

$y - 5=\frac{5}{2}(x - 8)$