Question

grade 8 - unit 3
georgias k-12 mathematics standards
name: ________________________ date: _______________
formative assessment

1. for each of the following relationships, describe what the graph would look like using

the following prompt:
\as the x - values ____, the y - values ____.\
a. positive association/correlation
b. negative association/correlation
c. no association/correlation

1. for each of the relationships above, produce an independent and dependent variable

that would create that relationship.

Explanation:

Step 1: Analyze Positive Association

In positive association, as one variable (x) increases, the other (y) also increases. So for part a, we fill in the blanks with "increase" for x - values and "increase" for y - values.

Step 2: Analyze Negative Association

In negative association, as the x - values increase, the y - values decrease. So for part b, we use "increase" for x - values and "decrease" for y - values.

Step 3: Analyze No Association

In no association, there is no consistent pattern. So as x - values change (increase or decrease), the y - values have no predictable pattern. So for part c, we can say "change (increase or decrease)" for x - values and "have no consistent pattern (increase, decrease, or stay the same randomly)" for y - values.

For question 2, we need to find independent and dependent variables for each relationship:

For Positive Association:

• Independent variable: Number of hours studied (x)
• Dependent variable: Test score (y). As the number of hours studied (x) increases, the test score (y) tends to increase.

For Negative Association:

• Independent variable: Number of hours spent watching TV (x)
• Dependent variable: Time spent on homework (y). As the number of hours spent watching TV (x) increases, the time spent on homework (y) tends to decrease.

For No Association:

• Independent variable: Shoe size (x)
• Dependent variable: IQ score (y). There is no association between shoe size and IQ score, so as shoe size (x) changes, IQ score (y) has no predictable pattern.

Answer:

1. a. As the x - values $\boldsymbol{\text{increase}}$, the y - values $\boldsymbol{\text{increase}}$.

b. As the x - values $\boldsymbol{\text{increase}}$, the y - values $\boldsymbol{\text{decrease}}$.
c. As the x - values $\boldsymbol{\text{change (increase or decrease)}}$, the y - values $\boldsymbol{\text{have no consistent pattern}}$.

1. a. Independent: Number of hours studied; Dependent: Test score

b. Independent: Number of hours watching TV; Dependent: Time on homework
c. Independent: Shoe size; Dependent: IQ score