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# Slope-intercept equation from slope & point

Video transcript

A line has a slope of negative
3/4 and goes through the point 0 comma 8. What is the equation of this
line in slope-intercept form? So any line can be represented
in slope-intercept form, is y is equal to mx plus b,
where this m right over here, that is of the
slope of the line. And this b over here, this is
the y-intercept of the line. Let me draw a quick
line here just so that we can visualize
that a little bit. So that is my y-axis. And then that is my x-axis. And let me draw a line. And since our line here
has a negative slope, I'll draw a downward
sloping line. So let's say our line
looks something like that. So hopefully, we're a little
familiar with the slope already. The slope essentially
tells us, look, start at some point
on the line, and go to some other point
of the line, measure how much you had to move in the
x direction, that is your run, and then measure
how much you had to move in the y direction,
that is your rise. And our slope is equal
to rise over run. And you can see over here,
we'd be downward sloping. Because if you move in
the positive x direction, we have to go down. If our run is positive,
our rise here is negative. So this would be a
negative over a positive, it would give you
a negative number. That makes sense, because
we're downward sloping. The more we go down
in this situation, for every step we
move to the right, the more downward
sloping will be, the more of a negative
slope we'll have. So that's slope right over here. The y-intercept just tells us
where we intercept the y-axis. So the y-intercept, this
point right over here, this is where the line
intersects with the y-axis. This will be the
point 0 comma b. And this actually just falls
straight out of this equation. When x is equal to
0-- so let's evaluate this equation, when
x is equal to 0. y will be equal to
m times 0 plus b. Well, anything times 0 is 0. So y is equal to 0
plus b, or y will be equal to b, when
x is equal to 0. So this is the point 0 comma b. Now, they tell us what
the slope of this line is. They tell us a line has
a slope of negative 3/4. So we know that our
slope is negative 3/4, and they tell us that the
line goes through the point 0 comma 8. They tell us we go through the--
Let me just, in a new color. I've already used orange,
let me use this green color. They tell us what we go
through the point 0 comma 8. Notice, x is 0. So we're on the y-axis. When x is 0, we're
on the y-axis. So this is our y-intercept. So b, we could say-- we could
do a couple-- our y-intercept is the point 0 comma 8, or we
could say that b-- Remember, it's also 0 comma b. We could say b is equal to 8. So we know m is equal to
negative 3/4, b is equal to 8, so we can write the
equation of this line in slope-intercept form. It's y is equal to negative
3/4 times x plus b, plus 8. And we are done.