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 $m$ is calculated using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can use two points on the line. Let's use the y - intercept $(0,3)$ and another point, say $(- 3,0)$ (where the line crosses the x - axis).
Substitute $x_1 = 0,y_1 = 3,x_2=-3,y_2 = 0$ into the slope formula:
$m=\frac{0 - 3}{-3-0}=\frac{-3}{-3}=1$

Step4: Write the equation

Substitute $m = 1$ and $b = 3$ into the slope - intercept form $y=mx + b$. We get $y=x + 3$.

Answer:

$y = x+3$