Question

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

Explanation:

Step1: Identify the y - intercept

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

Step2: Calculate the slope

We can use two points on the line, say $(- 8,0)$ and $(0,6)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-8,y_1 = 0,x_2 = 0,y_2=6$. Then $m=\frac{6 - 0}{0-(-8)}=\frac{6}{8}=\frac{3}{4}$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m = \frac{3}{4}$ and $b = 6$ into the equation, we get $y=\frac{3}{4}x+6$.

Answer:

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