Question

write the equation of this line in slope - intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest 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.

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

The line crosses the y - axis at $(0, - 4)$, so $b=-4$.

Step3: Calculate the slope ($m$)

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

Step4: Write the equation

Substitute $m = 1$ and $b=-4$ into $y=mx + b$.
We get $y=x-4$.

Answer:

$y = x-4$