Question

Jamie owns a house painting service. For each house, she charges $70 plus $40 per hour of work. A linear equation that expresses the total amount of money Jamie earns per house is y=70+40x. What are the independent and dependent variables? What is the y-intercept and the slope?

Select the correct answer below:

A. The independent variable (x) is the amount, in dollars, Jamie earns for a house. The dependent variable (y) is the amount of time Jamie paints a house.

Jamie charges a one-time fee of $40 (this is when x=0), so the y-intercept is 40. Jamie earns $70 for each hour she works, so the slope is 70.

Jamie charges a one-time fee of $40 (this is when x=0), so the y-intercept is 40. Jamie earns $70 for each hour she works, so the slope is 70.

B. The independent variable (x) is the amount, in dollars, Jamie earns for a house. The dependent variable (y) is the amount of time Jamie paints a house.

Jamie charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Jamie earns $40 for each hour she works, so the slope is 40.

Jamie charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Jamie earns $40 for each hour she works, so the slope is 40.

C. The independent variable (x) is the amount of time Jamie paints a house. The dependent variable (y) is the amount, in dollars, Jamie earns for a house.

Jamie charges a one-time fee of $40 (this is when x=0), so the y-intercept is 40. Jamie earns $70 for each hour she works, so the slope is 70.

Jamie charges a one-time fee of $40 (this is when x=0), so the y-intercept is 40. Jamie earns $70 for each hour she works, so the slope is 70.

D. The independent variable (x) is the amount of time Jamie paints a house. The dependent variable (y) is the amount, in dollars, Jamie earns for a house.

Jamie charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Jamie earns $40 for each hour she works, so the slope is 40.

Jamie charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Jamie earns $40 for each hour she works, so the slope is 40.

Step 1

**Independent and dependent variables in regression:**

In a simple regression, the variable of interest, regarding which, the prediction is being made, is the dependent or response variable; the variable which explains the variation in the response variable is the independent or predictor variable.

The slope of the equation is the rate of change of the dependent variable for unit increase in the independent variable.

Step 2

**Explanation:**

In this case, Jamie takes in initial fee of $70 for each house, irrespective of the number of hours worked. So, the intercept, that is, the value of *y* when *x* = 0 is 70.

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