CAN YOU THINK IN A LINE?

Insert your own names then try the following problems. If you can pick out the ones which will graph a line, you may be a top LINEAR BRAIN.

Answers are provided at the end.

and his sister are picking apples for the annual Christmas pie bake-off. He can pick three apples for every one that Tulip picks.

Is this a "linear" relationship when graphed?

says her favorite equation is, "y equals x squared."

Is this equation a line when graphed?

has a big fluffy St. Bernard dog named Tiny who eats five pounds of dog food every day.

If we graph the pounds of food eaten as the days pass, will this be a line?

plays his SUPER SYNTH electric guitar 2.5 hours each week day and then plays 4 hours per day on the weekend.

If we graph the hours played each week as the weeks pass, will it be a line?

challenges with this:

TRUE or FALSE
The equation y = 13.5x + 23.8x +(-45) is a line when graphed.

Then challenges with this:

TRUE or FALSE
The equation y = 3x^2 + 2x -13 is a line when graphed.

is a 110 pound wrestler on a diet. His coach says he can't wrestle as a "featherweight" unless he loses 2 pounds a day.

If keeps to this schedule, can we graph his total weight compared to the number of diet days as a line?

is scribbling a bit of Algebra on his desk in History class, because he wants to impress the hot babe who sits beside him. He just learned that all the best chicks require a boyfriend with a good brain, and he figures what better way to prove intelligence than Algebraic Mastery.

Here is the equation he scribbled:

y = 13(2/7)x^3 - 12.7x^2 +22x - 78

Will it be a line when he tries to graph it?

is writing a book of "Quizzles". He plans on becoming rich from his unique book of algebraic thought problems.

On page 32 we read, "The sum of three, consecutive, odd, integers is equal to 'y'." Graph this result.

Will it be a line?

is a physics teacher at a local high school. He puts the following equation on the board, -16x^2 + 123 = y.

asks his student to graph this equation for the class. Will she graph a line?

is a famous archeologist. She has a formula for determining the age of bones and artifacts. It looks like this,
age = 125.79x^2 + 11x -13.9

Will the equation be linear when graphed?

is working for the Grinch on a cleanup project this Christmas. For every ton of garbage she removes he will pay her $13.95.

Is the relationship of money earned compared to tons of garbage linear?

is a forensic scientist, like Scully on 'The X-Files'. can determine amazing things just from measuring certain bones. For example, a femur, (thigh bone) was recently unearthed when they tore down the Montgomery Ward's building to build a grocery store.

The bone was taken to a to see what she could determine. She was able to tell that it came from a person 5'8" tall. She used this formula: h=14.2f +7.

If she measured several femurs, and graphed their lengths and resulting heights would the graph be a line?

wants to know if square roots can generate linear equations. She types the following into her graphing calculator and tells it to graph. Does she get a line?

is a fortune teller who loves to pull algebraic tricks on customers. She tells that if the graph of is a line, he will be the winner of tons of money and a beautiful woman will enter his love life within the next week.

Does become rich?

is weaving a rug on a loom built by Amish, Indian women. Every time she pulls back her handle, 450 stitches are woven automatically onto the rug.

If we graph the number of pulls compared to the number of total stitches, will the graph be a line?

the gypsy peddler is selling popcorn balls. They have purple cotton candy wrapped around them and she is calling them "Purple Ice Balls from the Planet Korn". They are going for $.99 each.

If she graphs the amount earned compared to the number sold, will she get a line?

and are in training to become standup comedians. They are taking lessons at a local school named, 'Choose your Comedy like Your Life Depended on It Academy for the Humorously Gifted'.

Now they had to each pay a $75 registration fee and they each had to buy their own copy of 'The Book of Comedy' at $65.98. Their classes cost $7.50 per hour. If we graph the relationship of hours spent in class to total cost of education, will we get a line?

1.) c=3t...................yes linear

2.) y = x^2................no

3.) p = 5d................yes linear

4.) h = [2.5(5)+4(2)]w
.....h = [12.5+8]w
.....h = 20.5w..............yes linear

5.) y=13.5x+23.8x+-45 simplifies to
.....y=37.3x-45..........yes linear

6.) y=3x^2+2x-13.......no

7.) w=110-2d.............yes linear

8.) t=150+6.50h..........yes linear

9.) 13(2/7)x^3-12.7x^2+22x-78 no

10.) y=x+x+2+x+4
.......y=3x+6................yes linear

11.) -16x^2+123=y........no

12.) 125.79x^2+11x-13.9=y no

13.) m=$13.95t.............yes linear

14.) h=14.2f+7..............yes linear

15.) .............no

16.) ..............no

17.) s=450p.................yes linear

18.) e=$.99n................yes linear

19,) c=$75 +$65.98+$7.50h
.......c=$140.98 +$7.5h.....yes linear

***NOTE:

If you carefully examine the thing that all of the linear equations have in common, you will see that each one has both variables to the first power. In other words there are no exponents on the variables nor are there any square roots or absolute value bars around the variables.

These are called "first degree" equations because all the variables have an exponent of one. First degree equations will always graph as lines and thus are known as "linear equations."

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