Question

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 $(0,8)$, so $b = 8$.

Step2: Calculate the slope

We can use two points on the line. Let's take $(0,8)$ and $(1,6)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substitute $x_1 = 0,y_1 = 8,x_2 = 1,y_2 = 6$ into the formula:
$m=\frac{6 - 8}{1 - 0}=\frac{-2}{1}=- 2$

Step3: Write the equation

Substitute $m=-2$ and $b = 8$ into the slope - intercept form $y=mx + b$.
We get $y=-2x + 8$

Answer:

$y=-2x + 8$