Question

a line passes through point $(-2, 7)$ and has a slope of $-9$. write an equation in $ax + by = c$ form for this line. use integers for $a$, $b$, and $c$.

Explanation:

Step1: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Given that the point is $(-2,7)$ and the slope $m=-9$, we substitute these values into the point - slope form:
$y - 7=-9(x - (-2))$
Simplify the right - hand side: $y - 7=-9(x + 2)$

Step2: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, we have:
$y - 7=-9x-18$

Step3: Rearrange to $Ax + By = C$ form

Add $9x$ to both sides of the equation:
$9x+y - 7=-18$
Then add 7 to both sides:
$9x+y=-18 + 7$
Simplify the right - hand side:
$9x+y=-11$

Answer:

$9x + y=-11$