Question

he equation of the line in fully simplified slope-intercept 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 line crosses the y - axis at $(0,5)$, so $b = 5$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,5)$ and $(3,7)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1 = 5,x_2 = 3,y_2 = 7$ into the formula, we get $m=\frac{7 - 5}{3 - 0}=\frac{2}{3}$.

Step4: Write the equation

Substitute $m=\frac{2}{3}$ and $b = 5$ into the slope - intercept form $y=mx + b$.
We get $y=\frac{2}{3}x + 5$.

Answer:

$y=\frac{2}{3}x + 5$