Oh, and one other trick to have up your sleeve
Say you've got an equation in general form (ax + by = c), which is almost how your equations started out -- would just need to subtract the 3 in both cases to transport it to the other side of the equal sign.
Using the fact that the x-intercept occurs when y = 0, I can find the x-intercept as follows:
ax + b(0) = c ---> ax = c ---> x = c/a.
Using the fact that the y-intercept occurs when x = 0, I can find the y-intercept as follows:
a(0) + by = c ---> by = c ---> y = c/b.
Using the fact that the slope would be the coefficient of x if I were to translate this into general form, I can find it as follows:
ax + by = c ---> by = -ax + c ---> y = (-a/b)x + c/b.
So to summarize, given the equation of a line in general form ax + by = c,
your x-intercept is always c/a
your y-intercept is always c/b
your slope is always -a/b
I would consider it optional to memorize this, but it does save a couple steps sometimes!
Ashley Newman-Owens
GMAT Instructor
Veritas Prep
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