Question

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -6)$, so $b = -6$.

Step2: Calculate slope using two points

Use points $(0, -6)$ and $(6, -5)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$\displaystyle m=\frac{-5 - (-6)}{6 - 0}=\frac{1}{6}$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{1}{6}$ and $b=-6$.

Answer:

$\displaystyle y=\frac{1}{6}x - 6$