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 $(1, - 6)$.

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 $(x_2,y_2)=(1,-6)$. Then $m=\frac{-6 - 1}{1-0}=\frac{-7}{1}=-7$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - coordinate of the point where the line crosses the y - axis. From the point $(0,1)$, $b = 1$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m=-7$ and $b = 1$ gives $y=-7x + 1$.

Answer:

$y=-7x + 1$