Question

9 multiple choice 2 points ben researched the population of his town for each of the last ten years. he created a scatterplot of the data and noticed that the population increased by about the same amount each year. ben will determine the equation of the line of best fit for his data. which of the following statements about the equation of the line of best fit is true? the slope is zero. the slope is negative. the slope is positive. the slope is undefined.

Explanation:

Step1: Recall the meaning of slope

The slope of a line represents the rate of change. In a population - time scatter - plot, if the population increases over time, the rate of change is positive.

Step2: Analyze each option

• If the slope is zero, the population would remain constant. But the population is increasing, so this option is wrong.
• If the slope is negative, the population would be decreasing. But the population is increasing, so this option is wrong.
• If the slope is positive, it means as time (independent variable) increases, the population (dependent variable) increases. This is consistent with the given information.
• If the slope is undefined, the line is vertical. A vertical line would imply multiple populations at the same time, which is not the case for a population - time relationship.

Answer:

The slope is positive.