Question

write an equation for the line described. give the answer in standard form. through (2,3), m = -9 the equation of the line is \\(\square\\) (type your answer in standard form.)

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 $(x_1,y_1)=(2,3)$ and $m=-9$, we substitute these values into the point - slope form:
$y - 3=-9(x - 2)$

Step2: Expand the right - hand side

Using the distributive property $a(b - c)=ab - ac$, where $a=-9$, $b = x$ and $c = 2$, we get:
$y - 3=-9x+18$

Step3: Convert to standard form

The standard form of a line is $Ax + By=C$, where $A$, $B$, and $C$ are integers and $A\geq0$. We add $9x$ to both sides of the equation $y - 3=-9x + 18$:
$9x+y-3 = 18$
Then we add 3 to both sides:
$9x+y=21$

Answer:

$9x + y=21$