Question

a line has a slope of 6 and passes through the point (-2, -16). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

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 $m = 6$, so the equation is $y=6x + b$.

Step2: Substitute the point into the equation

We know the line passes through the point $(-2,-16)$. Substitute $x=-2$ and $y = - 16$ into $y=6x + b$:
\[

$$\begin{align*} -16&=6\times(-2)+b\\ -16&=-12 + b \end{align*}$$

\]

Step3: Solve for $b$

To solve for $b$, add 12 to both sides of the equation:
\[

$$\begin{align*} -16 + 12&=b\\ b&=-4 \end{align*}$$

\]

Step4: Write the final equation

Now that we know $m = 6$ and $b=-4$, substitute these values into the slope - intercept form $y=mx + b$. We get $y = 6x-4$.

Answer:

$y = 6x-4$