Question

a line passes through the point (-9, 3) and has a slope of \\(\frac{2}{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 $(-9,3)$, so $x_1=-9$ and $y_1 = 3$. The slope $m=\frac{2}{3}$.

Step3: Substitute values into the formula

Substitute $x_1=-9$, $y_1 = 3$ and $m=\frac{2}{3}$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 3=\frac{2}{3}(x+9)$ (since $x-(-9)=x + 9$).

Answer:

$y - 3=\frac{2}{3}(x + 9)$