Question

a line has a slope of -3 and passes through the point (6, -18). 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 $m=-3$, so the equation is $y=-3x + b$.

Step2: Substitute the point into the equation

We know the line passes through the point $(6,-18)$. Substitute $x = 6$ and $y=-18$ into the equation $y=-3x + b$:
$$-18=-3\times6 + b$$

Step3: Solve for $b$

First, calculate $-3\times6=-18$. Then the equation becomes:
$$-18=-18 + b$$
Add 18 to both sides of the equation:
$$-18 + 18=-18 + 18 + b$$
$$0 = b$$

Step4: Write the final equation

Since $m=-3$ and $b = 0$, the equation of the line in slope - intercept form is $y=-3x+0$, or simply $y=-3x$.

Answer:

$y = - 3x$