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 y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,-5)$, so $b=-5$.

Step3: Calculate the slope ($m$)

We can use two points on the line to find the slope. Let's take the y - intercept $(0, - 5)$ and another point on the line, say $(2,1)$ (we can see from the graph that when $x = 2$, $y=1$). The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Using $(x_1,y_1)=(0,-5)$ and $(x_2,y_2)=(2,1)$:
$m=\frac{1-(-5)}{2 - 0}=\frac{1 + 5}{2}=\frac{6}{2}=3$

Step4: Write the equation

Substitute $m = 3$ and $b=-5$ into the slope - intercept form $y=mx + b$.
We get $y = 3x-5$

Answer:

$y = 3x-5$