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CCSS Math: HSG.GPE.B.5

We're asked what is the
equation of line B? And they tell us that line A has
an equation y is equal to 2x plus 11. And they say that the
line B contains the point 6, negative 7. And they tell us lines A and B
are perpendicular, so that means that slope of
B must be negative inverse of slope of A. So what we'll do is figure out
the slope of A, then take the negative inverse of it. Then we'll know the slope of B,
then we can use this point right here to fill in the
gaps and figure out B's y-intercept. So what's the slope of A? This is already in
slope-intercept form. The slope of A is right there,
it's the 2, mx plus b. So the slope here
is equal to 2. So the slope of A is 2. What is the slope of B? So what is B's slope going
to have to be? Well, it's perpendicular to
A, so it's going to be the negative inverse of this. The inverse of two is 1/2. The negative inverse of
that is negative 1/2. So B's slope is negative 1/2. So we know that B's equation
has to be y is equal to its slope, m times x plus
some y-intercept. We still don't know what the
y-intercept of B is, but we can use this information
to figure it out. We know that y is equal
to negative 7 when x is equal to 6. Negative 1/2 times
6 plus b, right? I just know that this is on the
point, so this point must satisfy the equation
of line B. So let's work out what b must
be-- or what b, the y-intercept, this is a lowercase
b, not the line B. So we have negative 7 is equal
to-- what's negative 1/2 half times 6? That's not a b there,
that's a 6. What's negative 1/2 times 6? It's negative 3, is equal
to negative 3 plus our y-intercept. Let's add 3 to both sides of
this equation, so if we add 3 to both sides-- I just want to
get rid of this 3 right here-- what do we get? The left-hand side, negative
7 plus 3 is negative 4, and that's going to be equal to--
these guys cancel out-- that's equal to b, our y-intercept. So this right here
is a negative 4. So the equation of line B is y
is equal to-- its slope is a negative inverse of this
character-- so negative 1/2, negative 1/2 x. And its y-intercept we just
figured out is negative 4. And we are done.