Question

understand dependent and independent variables
quick review
think about how the values of variables affect each other.
to identify the dependent variable, ask yourself which variable depends on the other.
to identify the independent variable, ask yourself which variable causes the change.
examples
the spirit squad is washing cars. the equation m = 2c represents the money they make, m, for washing c cars. identify the dependent variable and the independent variable.
the amount of money the spirit squad makes depends on the number of cars they wash
the dependent variable is m.
the number of cars washed changes the amount of money made. the independent variable is c.
practice
identify the dependent variable and the independent variable in each situation.

1. the distance traveled, d, and the speed, s
2. the calories, c, in a snack and the amount of the snack, a
3. the amount of money you have spent, s, and how much money you have left, m
4. the number of apple slices remaining, r, and the number of apple slices eaten, e

lesson 4-9 use patterns to write and solve equations
quick review
look for patterns between two related variables to find rules and write equations.
example
write a rule and an equation that represents the pattern. then complete the table.

x	3	4	5	6	7
y	12	16	20	24	28

find the rule and write an equation
12 is 3 × 4
16 is 4 × 4
20 is 5 × 4
rule: the value of y is 4 times the value of x
equation: y = 4x
evaluate the equation for x = 6 and x = 7
y = 4 × 6 = 24
y = 4 × 7 = 28
practice

1. find the pattern and then write a rule and an equation that represents the pattern. then complete the table.

x	0	2	10	16	20
y	0	1	5

1. use the equation to complete the table

y = 6x + 1

x	1	2	3	4	5
y

topic 4 topic review 25

Explanation:

Step1: Analyze the pattern between x and y

Looking at the given table: when \( x = 0 \), \( y = 0 \); when \( x = 2 \), \( y = 1 \); when \( x = 10 \), \( y = 5 \). Let's check the ratio of \( y \) to \( x \): \( \frac{1}{2}=0.5 \), \( \frac{5}{10} = 0.5 \), \( \frac{0}{0}\) (undefined, but consistent with the pattern). So the rule is \( y=\frac{1}{2}x \) or \( y = 0.5x \).

Step2: Find y for x = 16

Substitute \( x = 16 \) into the equation \( y = 0.5x \). So \( y=0.5\times16 = 8 \).

Step3: Find y for x = 20

Substitute \( x = 20 \) into the equation \( y = 0.5x \). So \( y = 0.5\times20=10 \).

Answer:

For \( x = 16 \), \( y = 8 \); for \( x = 20 \), \( y = 10 \)