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Here’s an unshmoopy question you may find on your exam…
A line parallel to another line whose graph passes through the point (3, 8) and has a y-intercept
of -1 must have a slope of… what?
And here are the potential answers…
So… what is this question asking?
It’s all about lines – how well do we really know the point slope formula, y equals
mx plus b? Like… well enough to let it chinchilla-sit for us?
First of all, this whole “line is parallel” business is just the test-makers trying to
trip us up.
All parallel lines have the same slope, so let’s not fall prey to their wily schemes.
All we care about is the line passing through 3, 8 with a y-intercept of negative 1.
So in the y equals mx plus b format of describing a line, we have b already – it’s negative
1… the problem tells us that much.
Now we just have to solve for slope by taking what we know and plugging it into the base
equation.
y equals mx plus b… well, b is negative 1 so it’s:
y equals mx minus 1
But the problem GIVES us the point 3, 8, which we know the line passes through… so we can
simply plug in those points – 3 is x and 8 is y.
We get 8 equals m times 3 minus 1
Or, by adding 1 to each side, we have 9 equals 3m.
Our slope is 3… so our answer is C.
As in, “Chinchilla.”