Question

what is the equation of the line in standard form?
3x + y = 6
3x - y = -6
x - 6y = -9
x + 6y = 9

Explanation:

Step1: Calculate slope from points

Points are $(x_1,y_1)=(-3,1)$ and $(x_2,y_2)=(3,2)$.
Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{3-(-3)}=\frac{1}{6}$

Step2: Use point-slope form

Use point $(3,2)$: $y-y_1=m(x-x_1)$
$y-2=\frac{1}{6}(x-3)$

Step3: Convert to standard form

Multiply all terms by 6: $6y-12=x-3$
Rearrange to $Ax+By=C$: $x-6y=-9$

Step4: Verify with other point

Substitute $(-3,1)$ into $x-6y=-9$: $-3-6(1)=-9$, which holds true.

Answer:

$\boldsymbol{x - 6y = -9}$