Question

1. write the equation of the line represented by the following graph (2 points):

Explanation:

Step1: Find the slope

The line passes through points $(0, - 2)$ and $(3,0)$. The slope $m$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=-2,x_2 = 3,y_2 = 0$. So $m=\frac{0-(-2)}{3 - 0}=\frac{2}{3}$.

Step2: Find the y - intercept

The y - intercept $b$ is the y - coordinate of the point where the line crosses the y - axis. The line crosses the y - axis at $(0,-2)$, so $b=-2$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{2}{3}$ and $b = - 2$ into the equation, we get $y=\frac{2}{3}x-2$.

Answer:

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