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 y-intercept ($b$)

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

Step2: Calculate slope ($m$)

Use two points: $(0,6)$ and $(-3,4)$.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-6}{-3-0}=\frac{-2}{-3}=\frac{2}{3}$

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{2}{3}$ and $b=6$.
$y=\frac{2}{3}x+6$

Answer:

$y=\frac{2}{3}x+6$