Question

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

Explanation:

Step1: Identify two points

Let's take two points on the line, say $(0, - 5)$ and $(5,0)$.

Step2: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,-5)$ and $(x_2,y_2)=(5,0)$, we get $m=\frac{0 - (-5)}{5 - 0}=\frac{5}{5}=1$.

Step3: Determine the y - intercept

The y - intercept $b$ is the y - value when $x = 0$. From the point $(0,-5)$, we have $b=-5$.

Step4: Write the equation

The slope - intercept form is $y=mx + b$. Substituting $m = 1$ and $b=-5$, we get $y=x - 5$.

Answer:

$y=x - 5$