write the equation of the line in fully simplified slope - intercept form.

Answer:

$y = \frac{3}{4}x + 6$

Explanation:

Step1: Identify two points

Let's take two points on the line, say $(-8,0)$ and $(0,6)$.

Step2: Calculate the slope $m$

$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - 0}{0-(-8)}=\frac{6}{8}=\frac{3}{4}$

Step3: Identify the y - intercept $b$

The line crosses the y - axis at $(0,6)$, so $b = 6$.

Step4: Write the equation

Using the slope - intercept form $y=mx + b$, we get $y=\frac{3}{4}x+6$.