Question

a line has a slope of - 1 and passes through the point (-7, -10). 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 $m=-\frac{1}{7}$ and the point $(x,y)=(-7,-10)$.

Step2: Substitute values into the equation

Substitute $x=-7$, $y = - 10$ and $m=-\frac{1}{7}$ into $y=mx + b$. We get $-10=-\frac{1}{7}\times(-7)+b$.

Step3: Solve for $b$

First, simplify the right - hand side: $-\frac{1}{7}\times(-7) = 1$. So the equation becomes $-10=1 + b$. Then subtract 1 from both sides: $b=-10 - 1=-11$.

Step4: Write the equation

Substitute $m = -\frac{1}{7}$ and $b=-11$ back into $y=mx + b$. The equation of the line is $y=-\frac{1}{7}x-11$.

Answer:

$y =-\frac{1}{7}x-11$