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 the point $(0,4)$, so $b = 4$.

Step2: Calculate the slope

Choose two points on the line, say $(0,4)$ and $(1, - 2)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Then $m=\frac{-2 - 4}{1-0}=\frac{-6}{1}=-6$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y = mx + b$. Substituting $m=-6$ and $b = 4$ gives $y=-6x + 4$.

Answer:

$y=-6x + 4$