Question

a line passes through the point (9, 4) and has a slope of \\(\frac{4}{3}\\). 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 $(9,4)$, so $x_1 = 9$ and $y_1=4$. The slope $m=\frac{4}{3}$.

Step3: Substitute values into the formula

Substitute $x_1 = 9$, $y_1 = 4$ and $m=\frac{4}{3}$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 4=\frac{4}{3}(x - 9)$.

Answer:

$y - 4=\frac{4}{3}(x - 9)$