D. 3y-2x=3 ⇒ 2x-3y=-3
is the line that passes through (-3,-1) and (3,3).
What is the equation of a straight line passing through (x₁,y₁) and (x₂,y₂) ?
The equation of a straight line passing through (x₁,y₁) and (x₂,y₂) is a linear equation given by the formula
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
How to find the line going through (-3,-1) and (3,3)?
The equation of the line that goes through (-3,-1) and (3,3) is
[tex]\frac{y+1}{x+3}=\frac{3+1}{3+3}=\frac{4}{6}[/tex]
⇒ 6(y+1)=4(x+3)
⇒ 6y+6=4x+12
⇒6y-4x=6
⇒3y-2x=3
⇒2x-3y=-3
So, D is the correct option.
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