Question

a line has a slope of - 3 and passes through the point (7, - 17). 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 are given $m=-3$ and the point $(x = 1,y=-17)$.

Step2: Substitute values into the equation

Substitute $x = 1$, $y=-17$ and $m=-3$ into $y=mx + b$. We get $-17=-3\times1 + b$.

Step3: Solve for $b$

First, simplify the right - hand side: $-17=-3 + b$. Then, add 3 to both sides of the equation. So, $b=-17 + 3=-14$.

Step4: Write the equation of the line

Now that we have $m=-3$ and $b = - 14$, the equation of the line in slope - intercept form is $y=-3x-14$.

Answer:

$y=-3x - 14$