Question

a line has a slope of -9 and passes through the point (1, -3). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. We know that $m=-9$ and $(x_1,y_1)=(1, - 3)$. Substitute these values into the point - slope form: $y-(-3)=-9(x - 1)$.

Step2: Simplify the equation

Simplify the left - hand side: $y + 3=-9(x - 1)$. Then distribute the - 9 on the right - hand side: $y+3=-9x + 9$. Next, subtract 3 from both sides to get the slope - intercept form $y=mx + b$ (where $b$ is the y - intercept). So, $y=-9x+9 - 3$.

Step3: Combine like terms

Combine the constant terms: $y=-9x + 6$.

Answer:

$y=-9x + 6$