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Studying for a test? Prepare with these 4 lessons on Module 4: Linear equations.

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# Graphing proportional relationships from an equation

Video transcript

We're asked to graph y
is equal to 2.5 times x. So we really just have to
think about two points that satisfy this equation here,
and the most obvious one is what happens when x equals 0. When x equals 0, 2.5
times 0 is going to be 0. So when x is 0, y is
going to be equal to 0. And then let's just
pick another x that will give us a y that
is a whole number. So if x increases by 1, y
is going to increase by 2.5. It's going to go
right over there, and I could graph
it just like that. And we see just by
what I just said that the unit rate of change
of y with respect to x is 2.5. A unit increase in x, an
increase of 1 and x, results in a 2.5 increase in y. You see that right over
here. x goes from 0 to 1, and y goes from 0 to 2.5. But let's increase
x by another 1, and then y is going to increase
by 2.5 again to get to 5. Or you could say, hey, look,
if x is equal to 2, 2.5 times 2 is equal to 5. So this is a legitimate
graph for this equation, but then they also
tell us to select the statements that are true. So the first one is
the equation does not represent a proportional
relationship. Well, this is a
proportional relationship. A proportional
relationship is one where, first of all, if
you have zero x's, you're going to have zero y's, where y
is equal to some constant times x. And here, y is equal
to 2.5 times x. So this is definitely a
proportional relationship, so I'm not going to check that. The unit rate of the
relationship is 2/5. So I'm assuming--
this is a little ambiguous the way
they stated it. I'm assuming they're saying
the unit rate of change of y with respect to x. And the unit rate of change
of y with respect to x is, when x increases
1, y changed 2.5. So here they're saying when x
changes by 1, y changes by 0.4, 2/5 is the same thing as 0.4. This should be 5/2. 5/2 would be 2.4. So this isn't right as well. The slope of the line is 2.5. Well, this looks right. Slope is change in
y over change in x. When x changes 1, y changes 2.5. So change in y, 2.5,
over change in x, 1. 2.5 over 1 is 2.5. And you could also
see it looking at the form of
this equation. y is equal to-- this is
the slope times x. So that's right. A change of 5 units in x results
in a change of 2 units in y. Well, let's test that idea. We know when x is 0, y is 0. So if x goes from 0 to 5,
what's going to happen to y? Well, y is going
to be 2.5 times 5. 2.5 times 5 is 12.5. So y would not just change 2. It actually would change 12.5. So this isn't right. A change of 2 units in x results
in a change of 5 units in y. Well, we see that. A change in 2 units of x results
in a change of 5 units in y. That's exactly what we
graphed right over here. These two points show that. So this is definitely true.