Question

Convert y − 3 = 1/3(x − 6) to standard form.

A. x − 3y = 1
B. x − 3y = −3
C. x + 3y = 3
D. x + 3y = −1

Answer 1

The equation of a straight line in "standard form" resembles Ax + By + C = 0.

Starting with y − 3 = 1/3(x − 6) (which is the equation of a line in point-slope form), remove the fractional coefficient 1/3 by multiplying both sides of this equation by 3:

3y - 9 = x - 6.

We want all terms except for 0 to appear on one side of this equation. Subtract 3y from both sides, obtaining:

-9 = 1x - 3y - 6

Finally, add 9 to both sides, obtaining:

0 = 1x - 3y + 3

This result has the form Ax + By + C = 0, and is thus in standard form.