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 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 $(0, - 6)$, so $b=-6$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take the y - intercept $(0, - 6)$ and another point, say $(4, - 8)$ (by looking at the graph, we can see that when $x = 4$, $y=-8$). The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1,y_1)=(0, - 6)$ and $(x_2,y_2)=(4, - 8)$. Then $m=\frac{-8-(-6)}{4 - 0}=\frac{-8 + 6}{4}=\frac{-2}{4}=-\frac{1}{2}$.

Step4: Write the equation

Substitute $m =-\frac{1}{2}$ and $b=-6$ into the slope - intercept form $y=mx + b$. We get $y=-\frac{1}{2}x-6$.

Answer:

$y = -\frac{1}{2}x - 6$