Question

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

Explanation:

Step1: Identify slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
From the graph, we can see that the line crosses the y - axis at $(0,8)$, so $b = 8$.

Step2: Calculate the slope

We can use two points on the line to find the slope. Let's take the points $(0,8)$ and $(1,4)$. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1 = 8,x_2 = 1,y_2 = 4$ into the formula, we get $m=\frac{4 - 8}{1 - 0}=\frac{-4}{1}=- 4$.

Step3: Write the equation

Now that we have $m=-4$ and $b = 8$, substitute these values into the slope - intercept form $y=mx + b$.
We get $y=-4x + 8$.

Answer:

$y=-4x + 8$