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A line has a slope of 7
and goes through the point negative 4, negative 11. What is the equation of this
line in slope-intercept form? So the equation of any line
in slope-intercept form is y is equal to mx plus
b, where m is the slope and b is the y-intercept. Now, in this problem right
here, they tell us the slope. They tell us that a
line has a slope of 7. So we know right from the
get go that m is equal to 7. So we know the equation of this
line in slope-intercept form is going to look like y is
equal to, we know m is 7, so 7x plus-- let me
make that x a little bit neater-- 7x plus b. And now what we need to do,
we need to figure out b, and they give us one more
piece of information. They say that the line goes
through the point negative 4 comma negative 11. So that tells us that when
x is equal to negative 4, then y is equal to negative 11. So we can use this
information in what we have or the part of our
equation that we've been able to figure out so far. We know that when x is
equal to negative 4, y is going to be
equal to negative 11. So what b do we need
to make that happen? Let's try it out. So y is negative 11 when
x is equal to negative 4. So negative 11 is equal to
7 times x-- and in this case x is negative 4-- plus b. And now we can just solve for b. A b that makes this
equation, or that satisfies the constraint that
when x is equal to negative 4, y is equal to negative 11. So let's see, we get negative 11
is equal to 7 times negative 4 is negative 28
plus b, and now we can add a 28 to both
sides of this equation. So let's add a 28. I'm just trying to isolate
the b on the right-hand side. And so on the left-hand
side, negative 11 plus 28, that is just positive 17. These guys cancel
out on purpose. And I just have a b on
the right-hand side. So I get b is equal to 17. Let me write it in green. That's not green. We get b is equal to 17. So we know m is 7, they told
us that right at the beginning. And now we know b is 17. So the equation of
our line is y is equal to 7x, that's our slope. 7 times x plus b,
and b here is 17. And if we wanted to graph it, it
would look something like this. I'll just do a real rough graph. So if we wanted to graph
this line, that's my x-axis, and this is my y-axis. The y-intercept is 17. So that means that the
point 0, 17 is on this line. So this point right over
here is going to be 0, 17. And our slope is 7. So that means if we move to the
right one, we move up t seven. So it's a high slope. So if we move to the right
one, we move up seven. Or if we move back one,
will move down seven. So we'll move down
seven, so the line will look roughly like this. Obviously, haven't
done it very exactly, but our line is
going to look like. That's going to be a pretty
steep upward-sloping line. It has a very high
slope, slope of seven. If you move one in
the x direction, you have to move up seven. And its y-intercept
is at y is 17. When x is 0, y is 17.