Question

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

Explanation:

Step1: Identify two points on the line

Let's take the points (-6,0) and (0, - 7).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1=-6,y_1 = 0,x_2=0,y_2=-7$ gives $m=\frac{-7 - 0}{0-(-6)}=-\frac{7}{6}$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point (0,-7), $b=-7$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m =-\frac{7}{6}$ and $b=-7$ gives $y=-\frac{7}{6}x-7$.

Answer:

$y =-\frac{7}{6}x - 7$