Question

question 9 of 10, step 1 of 1 find the equation of the line in standard form that passes through the following points. eliminate any fractions and simplify your answer. (-9,11) and (3,-11)

Explanation:

Step1: Calculate the slope

Let $(x_1,y_1)=(-9,11)$ and $(x_2,y_2)=(3,-11)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-11-11}{3-(-9)}=\frac{-22}{12}=-\frac{11}{6}$

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$
Use $(x_1,y_1)=(-9,11)$:
$y-11=-\frac{11}{6}(x+9)$

Step3: Eliminate fractions

Multiply all terms by 6:
$6(y-11)=-11(x+9)$
$6y-66=-11x-99$

Step4: Rearrange to standard form

Standard form: $Ax+By=C$ (A positive integer)
$11x+6y=-99+66$
$11x+6y=-33$

Answer:

$11x+6y=-33$