Question

write the equation of this line in 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.

Step2: Find the y - intercept ($b$)

The line crosses the y - axis at $(0,5)$, so $b = 5$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,5)$ and $(8,1)$. The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1 = 5,x_2 = 8,y_2 = 1$ into the formula:
$m=\frac{1 - 5}{8 - 0}=\frac{-4}{8}=-\frac{1}{2}$

Step4: Write the equation

Substitute $m = -\frac{1}{2}$ and $b = 5$ into $y=mx + b$.
We get $y=-\frac{1}{2}x + 5$

Answer:

$y = -\frac{1}{2}x + 5$