Question

Write a linear equation in standard form for the line that goes through (2, -3)

Answer 1

9514 1404 393

Answer:

  C.  x -2y = 8

Step-by-step explanation:

One way you can do this is to use the form ...

  (Δy)(x -x1) -(Δx)(y -y1) = 0

where Δx = x2 -x1 = 4 -2 = 2, and Δy = y2 -y1 = -2 -(-3) = 1

This gives ...

  (x -2) -2(y -(-3)) = 0 . . . above form with numbers filled in

  x -2y -8 = 0 . . . . . . . general form

  x -2y = 8 . . . . . . . . .  standard form

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Additional comment

You can use any of several other strategies, including finding the slope and y-intercept, then rearranging the equation.

Another strategy that works is to try the answer choices. You might notice that the first given point works in the first equation, so it may make sense to try the second given point in each equation.

The above version of the equation of a line is a variation on one that says the slope of a line is the same everywhere:

  $\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y-y_1}{x-x_1}\ \Rightarrow\ (y_2-y_1)(x-x_1)=(x_2-x_1)(y-y_1)\\\\(y_2-y_1)(x-x_1)-(x_2-x_1)(y-y_1)=0$