Question

unit 1 review packet

1. write the slope - intercept form of each equation.

a. through (1, 3) and slope $=-\frac{2}{3}$

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. We know that the point is $(1,3)$ and the slope $m =-\frac{2}{3}$. Substitute $x_1 = 1$, $y_1=3$ and $m=-\frac{2}{3}$ into the point - slope formula:
$y - 3=-\frac{2}{3}(x - 1)$

Step2: Convert to slope - intercept form ($y=mx + b$)

First, distribute the $-\frac{2}{3}$ on the right - hand side:
$y - 3=-\frac{2}{3}x+\frac{2}{3}$
Then, add 3 to both sides of the equation. To add 3 (which is $\frac{9}{3}$) to $\frac{2}{3}$, we use the rule of adding fractions with the same denominator:
$y=-\frac{2}{3}x+\frac{2}{3}+\frac{9}{3}$
$y =-\frac{2}{3}x+\frac{2 + 9}{3}$
$y=-\frac{2}{3}x+\frac{11}{3}$

Answer:

$y =-\frac{2}{3}x+\frac{11}{3}$