hey it's Kaeleigh in this lesson we will be learning about the rise and run when
graphing in the coordinate plane make sure you've already done the lesson
about distance in the coordinate plane before starting this one let's get
started
we've learned how to find the distance between two points when they have the
same x-coordinate like these two or the same y-coordinate like these to remember
that we find the distance of each point from the axis between them and then we
add those distances together and that total distance is the distance between
two points now I have two sets of ordered pairs that have different
x-coordinates and different y-coordinates so what's the difference
the distance between these two points let's plot them to start point one is at
zero zero which we know is the origin so we can put it right there that's point
one at zero comma zero now point two is at
six comma five if we go over here to six on the x axis and up to five and that's
point two at six comma five well let's find the difference between the that
let's find the distance between the two x-coordinates here so if I know point
one is over here at zero and then my x-coordinate on point two is all the way
over here at six so we know the distance between our two x-coordinates is six now
what's the distance between our y-coordinates point one is over here at
zero point two is up here at five so I'm going all the way up here I have a
distance of five so now I only have one ordered pair here and I'm gonna go ahead
and plot it so it's a three on my x-axis and up to theirs point one now what if I
take my x-coordinate and I increase it by four and I'm gonna take my
y-coordinate and I'm gonna decrease it by three so three plus four my new point
is going to be seven for my x-coordinate and two minus three gives me negative
one for my y-coordinate so now let's go ahead and plot this so seven on my
x-axis and down one there's 0.2 so now I can see my change
in my x coordinate went from three all the way out here to seven that was a
change of four and my y-coordinate went from two down here to negative one and
that was a change of three so now I can say the distance between these would be
four for my x coordinate which I know here and three for my y coordinate which
is here nice work so now I'm gonna go ahead and
teach you what the vocabulary of these changes here are when we look at the
distance between two different x-coordinates it's called the run and
when we look at the distance between two different Y coordinates it's called the
rise now let's use these terms in practice so I have my point one here
which is that one comma one I'm gonna go ahead and plot it one on my x one on my
Y there's point 1 now I'm gonna say that I'm I have a run equal to four remember
a run is a change of my x coordinate so that means I'm going to add 4 here that
means my point two is going to live at 5 comma 1 which I can find that 5 on the X
x axis and 1 on my y-axis there's my new point 2 and I can see that I have a run
or the distance between my two points is 1 2 3 4 so the distance here or the run
is equal to 4 nice work so I have point 1 again at 1
comma 1 so it lives right there but now I have a rise
that's equal to negative six number rise is the distance between my my two
y-coordinates so I'm gonna and its negative so I have to subtract six here
for my y-coordinate so my x-coordinate stays this one my y-coordinate goes to
negative five so if I go ahead and I plot point to I'm gonna be over at one
my x-coordinate say it's the same but now I have to go down to negative five
and that's point two so now my rise was negative six so it came all the way down
here so this distance between my y-coordinates
is a distance of six downward nice work what is the rise and the run between
these two points this means we need to find the change in the y-coordinate and
the change in the x coordinate between these two points to do this we always
start with the point with the smallest x coordinate that is the same as saying
always start with the point that is the furthest to the left on the coordinate
plane now let's find the rise and the run between these two points remember we
always start with the smallest x coordinate so I'll call this point 1 and
this point 2 and we'll travel up to find point 2 so to find the distance between
these two points I'm going to find my rise which is the difference of mono
y-coordinate so I'm going to go up on the y-axis until I meet the same
y-coordinate as point two here so this here is my rise my change my
y-coordinate and then I start here at x-coordinate one and I'm going to travel
over to point two so this here is my run so let's find what is our
is so the rise here I have two options either I can count one two three how
many boxes I go up so that would give me a rise of 3 but the other thing is I can
do is I can find the difference in my Y coordinates between point 1 and point 2
so that would tell me this point here is that 1 1 and this point here is at 3
comma 4 so my rise could also be my for the y coordinate over here minus 1 the y
coordinate from over here equals 3 it's now the change in my run I can do the
same thing I can count how many boxes I went through 1 2 or I can find the
difference in my x coordinate which would be this 3 minus this 1 here 1 is
equal to 2 so there's two different ways to find the rise and the run nice work
you get to practice finding the rise and the run on your own by doing the online
games and quizzes have fun and remember to always be clever