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 passes through the origin $(0,0)$, so $b = 0$.

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 take the points $(0,0)$ and $(6,4)$.
Substitute $x_1 = 0,y_1 = 0,x_2 = 6,y_2 = 4$ into the slope formula:
$m=\frac{4 - 0}{6 - 0}=\frac{4}{6}=\frac{2}{3}$

Step4: Write the equation

Substitute $m=\frac{2}{3}$ and $b = 0$ into the slope - intercept form $y=mx + b$.
We get $y=\frac{2}{3}x+0$, which simplifies to $y=\frac{2}{3}x$

Answer:

$y=\frac{2}{3}x$