Question

1. error analysis a student claims that if y - values are not increasing as x - values increase, then the data must show a negative association. explain the error the student made.
2. vocabulary in a scatter plot that shows a positive association, describe how y - values change as x - values increase.
3. make sense and persevere does a trend line need to pass through all the points in a scatter plot? explain.
4. communicate precisely describe how the point - slope formula is useful when writing the equation for a trend line.
5. describe the type of association between x and y for the set of data. explain.
6. describe the type of association between x and y for the set of data. explain.

Explanation:

2.

The student's error is that when y - values are not increasing as x - values increase, it could also mean there is no association (data points are randomly scattered) rather than just a negative association where y - values decrease as x - values increase.

3.

In a scatter - plot with a positive association, as x - values increase, y - values also tend to increase.

4.

A trend line does not need to pass through all the points in a scatter - plot. It is a line that best represents the general pattern of the data, minimizing the distance between the line and the data points.

5.

The point - slope formula \(y - y_1=m(x - x_1)\) is useful when writing the equation for a trend line because if you know the slope \(m\) of the trend line and a point \((x_1,y_1)\) on the line, you can easily write the equation of the line.

6.

The scatter - plot shows a positive association. As x - values increase from left to right, y - values generally increase.

7.

The set of data shows a negative association. As x - values increase (from 4 to 10), y - values generally decrease (from 9 to 3).

Answer:

2.

The student ignored the possibility of no association.

3.

y - values tend to increase.

4.

No, it represents the general pattern.

5.

Use slope and a point to write the equation.

6.

Positive association; y - values increase with x - values.

7.

Negative association; y - values decrease as x - values increase.