This is how the question reads: "The equation of the line that goes through the points (3, -6) and (3, 10) can be written in general form Ax + By + C = 0 where A = _ B = _ and C = ____" I know the answer for B is 0 but am unable to find the solutions for A and B. Please help!
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$\begingroup$This is a vertical line since it passes through two points with the same horizontal coordinate ($3$). Vertical lines always have an equation of the form $x=k$. In this case, $k=3$ by inspection. In your general form this is
$$1x-0y-3=0,$$
right?
Addendum: It would be very much worth your time to memorize the fact that vertical (horizontal, resp.) lines have equations of the form $x=k$ ($y=k$, resp.), and that they are characterized by the fact that all points on them have the same horizontal (vertical, resp.) coordinate.
$\endgroup$ 5 $\begingroup$This appears to be a vertical line. The x-coordinate is always equal to $3$, so we can write $x=3$. This is in fact the equation of the line. Let's put it into general form.
$$ \begin{align} &x=3 \\ &x-3=0 \\ &1x-0y-3=0 \\ \end{align} $$
Therefore $A=1$, $B=0$ and $C=-3$.
$\endgroup$ 3 $\begingroup$This is another example of procedures getting in the way of common sense.
Plot the points $(3, -6)$ and $(3, 10)$ on a Cartesian plane. Did you notice that a line through these points is just a vertical line where $x=3$? Rearranging into the form of $Ax+By+C=0$, we have $1x+0y+(-3)=0$.
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