Question

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

Explanation:

Step1: Find two points on the line

The line passes through (0, 1) and (1, - 3).

Step2: Calculate the slope $m$

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(1, - 3)$. Then $m=\frac{-3 - 1}{1 - 0}=\frac{-4}{1}=-4$.

Step3: Use the slope - intercept form $y = mx + b$

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m=-4$ and from the point $(0,1)$, when $x = 0$, $y = 1$, so $b = 1$.

Step4: Write the equation of the line

Substitute $m=-4$ and $b = 1$ into $y=mx + b$. The equation of the line is $y=-4x + 1$.

Answer:

$y=-4x + 1$