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today we're going to be using a table to graph a line
last week
we did this
only we used the equation y equals mx
and we use that equation to create a table and graph the line representing
that equation
this week we will be looking at the equation y equals m x plus b
so now there is going to be something added or subtracted on the end
so what we're going to do today
is take this equation again
create a table and then use that table
to plot the points
draw in the line
so let's go ahead and get started here
now last week when we did creating a table
we were given x values already
this week we're going to put in our own x values
you can pick whatever x values you want to
but i suggest picking x values that are close to zero
you can pick an x value of five hundred
but if i pick an x value of five hundred then you need to plot that in the graph
so i suggest picking smaller numbers that are close to zero
i always like to do a few negatives and a few positive intergers
so i usually do -2
-1
0, 1, and 2
these are the x-values I usually choose
when making a table
they're close to zero
including zero
and easier to plugin to get
y-values so i can plot these points
let's go ahead and fill these x-values now
and find the missing y-values
the first x-value equals -2, we need to plug this
remember that means we substitute that right in for the x there
so we're going to get
y equals -3 times
now remember we are going to substitute -2 right in right in
so, y equals -3 times -2
plus 4
all right so that we can simplify to stop
negative times a negative is a positive
so -3 times -2
give us positive 6
plus four
6 + 4 = 10
so with an x-value of -2 we get a y-value of 10
same thing for the next one let's put -1 here
y equals -3 times -1
now again, we just replace the x with -1
then plus 4
notice how the -3 and the plus 4 do not change
those are constant in our equation
we only change our x-value each time
similar to last time we simplify this
and -3 times -1 gives me
a positive 3
plus four
3 + 4 = 7
so when my x-value is -1
i get a y-value of 7
onto the next one here
y equals -3 times my x-value of 0 plus 4
plus four
now remember anything time zero is zero
0 + 4 = 4
so when x=0 the y=4
all right
next one here negative three times the x-value, 1, plus 4
now a negative times a positive is a negative
so, -3 time 1 is -3
plus 4
-3 + 4
remember when it's negative
we really subtract four minus three which is 1
and since the 4 is larger and that is positive, the 1 will be positive
so when the x-value is 1 the y-value is 1 in this equation
last x-value we're going to plug in is 2
y equals -3 times 2
plus 4
again a negative times a positive is negative
-3 times 2
gives me -6
plus four
-6 + 4
six minus four gives me 2
since the six is larger and it is negative
the 2 will be negative as well
so this is -2
when the x-value is 2 the y-value is -2
now we have our table completed
remember what this gives us is ordered pairs, an x and a y-value
so now we have these ordered pairs (-2, 10)
(-1, 7)
(0, 4)
(1, 1)
(2, -2)
now we are going to take these ordered pairs
and we are going to plot the points to graph this line
(-2, 10) means
we go left 2
and up 10
so count it out left 2
and up 10
there is our first point
(-1, 7) means I go to the left 1
and up seven
counting it out and there is our second point
(0, 4)
zero right or left and up 4
there is our third point
(1, 1)
so to the right one and up 1
notice how these are lying in a straight line as i plot these
last one, (2, -2)
to the right 2 and down 2
remember we are graphing a linear equation
so if any of your points do not lie in a straight line
if one of my points was way out here
then i would know that i had to go back and recheck my math over here because
they have to be in a straight line
now after i plot my points
again i'm going to take my line function
and run the best line that i can
going right through those
and there is our line
from the table
so that's my line
representing the equation y= -3x+4
if you have any questions
please give me a call