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 ($b$)

From the graph, the line crosses the y - axis at $(0,-3)$. So, $b=-3$.

Step3: Calculate the slope ($m$)

We can use two points on the line. We know the y - intercept is $(0, - 3)$ and we can see that the line also passes through $(4,0)$. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,-3)$ and $(x_2,y_2)=(4,0)$. Then $m=\frac{0 - (-3)}{4 - 0}=\frac{0 + 3}{4}=\frac{3}{4}$.

Step4: Write the equation

Substitute $m = \frac{3}{4}$ and $b=-3$ into the slope - intercept form $y=mx + b$. We get $y=\frac{3}{4}x-3$.

Answer:

$y=\frac{3}{4}x - 3$