Find the missing coordinate for the line through (–13, 2) and (x, –4) with a slope of − 2/ 3 .
To do this problem requires an understanding of the meaning of SLOPE.
SLOPE is the difference, found by subtraction, of the y-coordinates divided by the difference of the x-coordinates. Using that definition we can set up an equation. By the way, division can be shown by a fraction.
–2 –4 – 2 –6
___ = ___________ = _______
3 x – (–13) x + 13
Now we can use cross-multiplication to get rid of the fractions and have an easier equation to solve. You can also solve this by multiplying the first fraction by 3 and then setting the denominators equal to one another since the numerators are equal. However, cross-multiplying is a more universal strategy, so I'll use it.
–2 –6
____ = _____
3 x + 13
(–2)(x + 13) = (3)(–6)
–2x – 26 = –18
Now add 26 to each side.
–2x – 26 = –18
–2x – 26 + 26 = –18 + 26
–2x = 8
Now divide each side by (–2).
–2x = 8
–2x 8
____ = ____
–2 –2
x = –4
