Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. From the graph, the line crosses the y - axis at $(0, - 4)$, so $b=-4$.

Step2: Calculate the slope

We can use two points to find the slope. Let's take the points $(0, - 4)$ and $(3, - 6)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 0,y_1=-4,x_2 = 3,y_2=-6$ into the formula: $m=\frac{-6-(-4)}{3 - 0}=\frac{-6 + 4}{3}=\frac{-2}{3}$.

Step3: Write the equation

Substitute $m =-\frac{2}{3}$ and $b=-4$ into the slope - intercept form $y=mx + b$. We get $y=-\frac{2}{3}x-4$.

Answer:

$y =-\frac{2}{3}x - 4$