Question

Indicate the equation of the line meeting the given conditions. Put the equation in standard form.

Containing C(3,3) and D(-3,2).

Answer 1

x -6y = -15

Explanation:

There are several ways we can get from the given points to a standard-form equation for the line through them. One way is to equate the slope from a general point (x, y) to point C with that of the slope from point D to point C.

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The slope of a line between two points is ...

m = (y2 -y1)/(x2 -x1)

From (x, y) to C:

m = (y -3)/(x -3)

From D to C:

m = (2 -3)/(-3 -3) = -1/-6 = 1/6

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Equating these slopes, we have ...

(y -3)/(x -3) = 1/6

6(y -3) = (x -3) . . . . . multiply by 6(x -3)

6y -18 = x -3 . . . . . . eliminate parentheses

x -6y = -15 . . . . . . . add 3-6y

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Additional comment

The standard form equation of a line is ...

ax +by = c

where a > 0, and 'a', 'b', 'c' are mutually prime integers.

Usually, we like to have the variables in lexicographical order, so the first term will be the x-term, and its coefficient will be positive.