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. Given $m=-5$, so the equation is $y=-5x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 1,y=-9)$ into $y=-5x + b$. We get $-9=-5\times1 + b$.

Step3: Solve for $b$

Simplify the right - hand side: $-9=-5 + b$. Add 5 to both sides of the equation: $b=-9 + 5=-4$.

Step4: Write the final equation

Substitute $b = - 4$ back into $y=-5x + b$. The equation of the line in slope - intercept form is $y=-5x-4$.

Answer:

$y=-5x - 4$