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: 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 y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,3)$, so $b = 3$.

Step3: Calculate the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can use two points on the line. Let's use the y - intercept $(0,3)$ and the x - intercept $(- 4,0)$.
Substitute $x_1=-4,y_1 = 0,x_2 = 0,y_2=3$ into the slope formula:
$m=\frac{3 - 0}{0-(-4)}=\frac{3}{4}$

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:

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