Question

a line has a slope of -5 and passes through the point (1, -9). 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 $m=-5$, so the equation is $y=-5x + b$.

Step2: Substitute the point into the equation

We know the line passes through the point $(1,-9)$. Substitute $x = 1$ and $y=-9$ into the equation $y=-5x + b$:

$$
LATEXBLOCK0
$$

Step3: Solve for $b$

To solve for $b$, add 5 to both sides of the equation:

$$
LATEXBLOCK1
$$

Step4: Write the final equation

Now that we know $m=-5$ and $b = - 4$, substitute these values into the slope - intercept form $y=mx + b$:
$y=-5x-4$

Answer:

$y = - 5x-4$