Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest for

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The line crosses the y - axis at $(0,4)$, so $b = 4$.

Step3: Calculate the slope ($m$)

We can use two points on the line. We know the y - intercept is $(0,4)$ and another point on the line is $(- 6,0)$. The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(-6,0)$. Then $m=\frac{0 - 4}{-6 - 0}=\frac{-4}{-6}=\frac{2}{3}$.

Step4: Write the equation

Substitute $m=\frac{2}{3}$ and $b = 4$ into the slope - intercept form $y=mx + b$. So the equation is $y=\frac{2}{3}x + 4$.

Answer:

$y=\frac{2}{3}x + 4$