Chapter 5 Review

Dependent and Independent Variables:

 

The dependent variable depend on the independent variable.


EXAMPLES:

 

1. Weight of a Car (Independent) & Fuel Consumption (Dependent)

 

2. Oranges (Independent) & Amount of Orange Juice (Dependent)

 

3. Number of bicyclers (Dependent) & Temperature Outside (Independent)

 

An easy way to figure this out is to try and put it in a sentence (i.e. "the amount of orange juice depends on the amount of oranges" makes more sense than "the amount of oranges depends on the amount of orange juice)

 

The Independent variable goes on the X axis and the Dependent variable goes on the Y axis.

 

SCATTER PLOT GRAPHS

 

Scatter plot graphs are mainly useful for identifying relationship.

 

Outlier: A number that is distant, or looks like it is not related to the data. Similar to "The Odd One Out."

 

Infirrence: A conclusion drawn from a scatter plot graph.

 

SLOPE

 

- Slope is the change in y over the change in x. In other words it is how you measure the         distance from two points on a graph.

 

- For example if there is one point (2,3) and another point (4,9), the slope of the line               connecting those two points is 3.

 

- In order to find the slope you have to know the formula y2-y1/x2-x1. So let’s go through that   question step by step.

 

-       First you put in the values- 9-3/4-2

-       Solve each side- 6/2

-       Then simplify- 3

 

- In that question 9 was y2, and 3 was y1, where 4 was x2, and 2 was x1

 

- In order to know where to put each value, remember this for the two points- point1 =(x1,y1),   point 2 =(x2,y2)

 

- Note- divide the number down to the lowest possible without getting a decimal

 

Example of a Slope


 

DIRECT AND PARTIAL VARIATION

 

- To find the equation of a line segment you use 2 equations, y=mx, and y=mx+b.

 

- Here m=slope and b=the value of y when x is 0

 

- You use y=mx for direct variations and y=mx+b for partial variations.

 

- The difference between direct and partial variations is that in a direct variation, when y is 0,   x is also 0, in other words the line segment passes through the point (0,0). A partial             variation is  a line segment that never passes through the point (0,0), in other words, when     x is 0, y is not.

 

Example of direct is y=2x, example of partial is y=3x+5, in this case when x is 0, y is 5

 

 

RATE OF CHANGE

 

- The rate of change is the continuous difference between a set of points, or in other words, the slope of a line segment.

 

- If you have an equation of a line y=3x+2, the rate of change is 3

 

- Heres a chart for example

 

 

- Therefore the rate of change is 4

 

- Note- a slope in an equation is a constant rate of change

 

REVIEW

 

Find the slope of the following points

 

a) (3,6)(4,8)

b) (4,9)(7,12)

c) (16,17)(19,24)

d) (101,45)(100,50)

e) (25,-23)(27,21)

 

Using the answers of the first question and the first point given find if the line is a direct or partial variation

For example- (3,4)(5,8) have a slope of 2

-       Next step is put 3,4 and 2 into y=mx+b

-       4=3(2)+b

-       4=6+b

-       4-6=b

-       B=-2

-       There fore it is a partial variation

 

Determine the rate of change for the following points

 

a) (3,4)(4,6)(5,8)

b) (4,6)(6,12)(8,18)

c) (1,2)(2,3)(4,5)

d) (4,6)(7,12)(12,22)

 

Determine if the following points have a constant rate of change

 

a) (4,5)(5,8)(6,11)

b) (5,6)(6,9)(7,11)

c) (2,4)(5,5)(8,6)

d) (22,16)(45,39)(68,63)

 

Quick Review

Slope

-       y2-y1/x2-x1 (change in y over change in x)

-       used to find steepness of line segment

-       line joining (5,7)(8,10) which becomes 10-7/8-5 which becomes 3/3 which becomes 1

 

Direct and partial variation

-       2 different forms of equations

 

Direct

-       When x is 0, so is y (b has no value)

-       Y=2x

 

Partial

-       When x is 0 y is not (b has a value)

-       Y=2x+3

 

First differences

-       The constant slope between a set of points

 


Practice Test


Find the slopes of the following points

a)     (8,9)(5,8)

b)    (6,13)(24,21)

c)     (12,24)(24,36)

d)    (53,64)(23,78)

e)     (12,23)(12,25)

f)     (21,34)(107,234)

 

Verify if the equation is a direct or partial variation

a)     Y=2x+5

b)     Y=3x

c)     Y=1/4x-22

d)     Y-x=0

e)     Y-3x=24

 

3. Using your answers from question 1, make an equation for each slope, then find out if     it is a direct or partial variation

 

a)     Make an equation for the line segment joining (3,6)(4,12)

b)     Determine if this is a direct or partial variation

c)     Make a table displaying the data from x=1 to x=5

d)     find the first difference for these points

e)     Graph part c

f)     Find the second difference (difference between first differences

 

a) Fill out the table (note the fist difference here is constant for all points)

X

Y

1

7

2

14

____

28

5

____

____

63

12

____

____

119

15

____

-13

____

 

b)    Is this a partial or direct variation?