Chapter 2 and 3

Solving Linear Equations

100

Solve for x:

3x-6=12

x=6

200

Solve for y:

3y+2x=15

y=-2/3*x+15

300

Solve for x:

ax+by=cz

x=c/a*z-b/a*y

400

Solve for x:

5x+7=2x+28

x=7

500

Solve for y:

15x-2y=7y+25

y=3x-5

Linear Functions

100

Define slope.

This slope is then the amount the function changes when the variable increases by 1 unit.

m=(y₂-y₁)/(x₂-x₁)

200

What is the format of a linear function?

y=mx+b

300

Do these data points represent a linear function?

(0,2), (1,6), (2,10), (3,14)

Yes.

(6-2)/(1-0)=4

(10-6)/(2-1)=4

...

400

Do these data points represent a linear function?

(0,2), (1,3), (2,6), (3,11)

No.

(3-2)/(1-0)=1

(6-3)/(2-1)=3

(11-6)/(3-2)=5

500

Find the equation of the line with a slope of 3 passing through the point (2,5).

y=3x-1

Use y=mx+b:

5=(3)(2)+b

5=6+b

-1=b

Solving Non-Linear Equations

100

Solve for x:

x²-4=0

x=2

x=-2

200

Solve for x:

x³-8=0

x=3

300

Solve for y:

y²-x=14

y=(x+14)^1/2

y=-(x+14)^1/2

400

Use the crossing graphs method to solve:

x²+2=18

on the interval [0,5].

x=4

500

Use the crossing graphs method to solve:

x³-3x+6=8

on the interval [0,5].

x=2

Misc.

100

When is a set of data linear?

When the rate of change between all the points is constant.

200

How would you describe the slope of a decreasing line?

Negative.

300

Solve for x:

2^x=8

x=3

400

Find the linear equation for this data:

(0,2), (1,6), (2,10), (3,14)

y=4x+2

500

Is this data concave up or down on the interval [0,4]?

(0,2), (1,3), (2,6), (3,11)

Concave up, because the rate of change between the points in increasing and getting larger.