Question

Marc owns a landscaping business. For each lawn, he charges $75 plus $30 per hour of work. A linear equation that expresses the total amount of money Marc earns per lawn is y=75+30x. 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 of time Marc works a property. The dependent variable (y) is the amount, in dollars, Marc earns for a lawn.

Marc charges a one-time fee of $75 (this is when x=0), so the y-intercept is 75. Marc earns $30 for each hour he works, so the slope is 30.

B. The independent variable (x) is the amount of time Marc works a property. The dependent variable (y) is the amount, in dollars, Marc earns for a lawn.

Marc charges a one-time fee of $30 (this is when x=0), so the y-intercept is 30. Marc earns $75 for each hour he works, so the slope is 75.

C. The independent variable (x) is the amount, in dollars, Marc earns for a lawn. The dependent variable (y) is the amount of time Marc works a property.

Marc charges a one-time fee of $30 (this is when x=0), so the y-intercept is 30. Marc earns $75 for each hour he works, so the slope is 75.

D.The independent variable (x) is the amount, in dollars, Marc earns for a lawn. The dependent variable (y) is the amount of time Marc works a property.

Marc charges a one-time fee of $75 (this is when x=0), so the y-intercept is 75. Marc earns $30 for each hour he works, so the slope is 30.

Answer 1

Simple linear regression

We know that for independent variable x and dependent variable y, the regression equation is given by y= a+bx where a is the y-intercept and b is the slope of the equation.

So here the independent variable (x) is the amount of time, in hours, Marc works for a property. The dependent variable (y) is the amount, in dollars, Marc earns for a lawn.

Marc charges a one-time fee of $75 (when x=0), so the y-intercept is 75. Marc earns $30 for each hour he works, so the slope is 30.

Thus A is the correct answer.