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 the y - intercept

The line crosses the y - axis at the point $(0, - 7)$. So, $b=-7$.

Step2: Calculate the slope

Pick two points on the line, say $(0, - 7)$ and $(8,1)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=-7,x_2 = 8,y_2 = 1$. Then $m=\frac{1-(-7)}{8 - 0}=\frac{1 + 7}{8}=\frac{8}{8}=1$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substitute $m = 1$ and $b=-7$ into the equation. We get $y=x - 7$.

Answer:

$y=x - 7$