Question

write the equation of the line in fully simplified slope - intercept 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 line crosses the y - axis at $(0,6)$, so $b = 6$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,6)$ and $(5,8)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1 = 6,x_2 = 5,y_2 = 8$ into the formula:
$m=\frac{8 - 6}{5 - 0}=\frac{2}{5}$

Step4: Write the equation

Substitute $m=\frac{2}{5}$ and $b = 6$ into $y=mx + b$.
We get $y=\frac{2}{5}x+6$

Answer:

$y=\frac{2}{5}x + 6$