Question

Determine the standard form of the equation of the line that passes through (6,0) and (2,-7).

Answer 1

Answer:

-7x + 4y = +42

Step-by-step explanation:

Going from point (2, -7) to point (6, 0), x increases by 4 and y increases by 7.  Thus, the slope of the line in question is m = 7/4.

Starting from the equation y = mx + b, and subbing (7/4) for m, 6 for x and 0 for y, we get:

0 = (7/4)(6) + b.  Then b = 42/4, or 21/2.  Thus, we now have y = (7/4)x + 21/2.

We must put this into "standard form."  Multiplying all three terms by 4, we get:

4y = 7x + 42.  Rearranging these terms to fit the "standard form" equation Ax + By = C, we get:

-7x + 4y = +42