MONDAY, December 1, 2014
Entry 162: Warm-Up
Make a rule for each of Barbara’s animals.
Barbara has a bunny that weighs 5 pounds and gains 3 pounds per year.
Her cat weighs 19 pounds and gains 1 pound per year.
Entry 163: Animal Intersection
Make a table to track Barbara’s pets’ weights for 8 years.
Bunny:
x (years)
0
1
2
3
y (weight)
4
5
6
7
8
Cat:
x (years)
0
1
2
3
4
5
6
7
8
y (weight)
When do you think that Barbara’s Bunny and Cat will be the same weight?
Graph both of their rules on the same axes.
Did you get an intersection at the same point as in the tables?
This means that the two rules are equivalent at this point.
Entry 164: Equal Values Method
Since we know that lines are equivalent at certain points, this mean they are equal at certain points.
We write all our rules as 𝑦 = 𝑚𝑥 + 𝑏, so we can set them equal to each other. This is called the Equal Values Method.
Ex.
We can say this because we know
Does 𝑦 = 𝑦?
𝑦 = 3𝑥 + 5
that they are equivalent at one or
So if 𝑦 = 3𝑥 + 5 and 𝑦 = 𝑥 + 19 and 𝑦 = 𝑦, can
more points since they are not
𝑦 = 𝑥 + 19
we say that 3𝑥 + 5 = 𝑥 + 19?
parallel.
Setting the equations
equal to each other
and solving for x will
tell us exactly what xcoordinate they are
equivalent at.
3𝑥 + 5 = 𝑥 + 19
2𝑥 = 14
𝑥=7
So we know that the equations are
equivalent at 𝑥 = 7
We want to find out at exactly what point the
equations are equivalent. A point is in the form
(x,y). We have already found x, so we need to find
y.
We find y by plugging in the x that we found into
an original equation and then solve for y.
𝑦 = 3(7) + 5
After plugging in x, and solving for y, we have found that the equations are equivalent at
𝑦 = 21 + 5
the point (7, 26)
𝑦 = 26
Find the point where the two lines intersect and are equivalent.
a. 𝑦 = 2𝑥 + 3
b. 𝑦 = −3𝑥
c. 𝑦 = 𝑥 + 2
𝑦 =𝑥+4
𝑦 = −𝑥 + 8
𝑦=6
Entry 165: Homework 5-48 // 5-49 // 5-51
5-48. Graph the line 𝑦 = 2𝑥 − 3 and 𝑦 = −𝑥 + 3.
a. Where do they intersect? Label the point on the graph.
b. Find the point of intersection using the Equal Values Method. That is, start by combining both equations into one equation
that you can solve for x.
c. Which method is easier, graphing or using algebra to solve?
5-49. Solve for the variable.
7𝑦
3𝑦
11
a.
− =
b.
8
𝑎+4
3
5
𝑎
2
𝑎+7
7
5
− =
5-51. Janelle came to bat 464 times in 131 games. At this rate, how many times should she expect to have at bat in a full season of
162 games?