Question

Alyssa works as a sales representative in an electronics store. She earns a fixed daily wage plus a commission on the sales she makes. The table shows her earnings based on the amount of sales she makes in a day.
Total Sales ($) Daily Earnings ($)
0 80
200 110
500 155
800 200
1,200 260

The equation that gives Alyssa's daily earnings based on her total sales is_____ .

When this data is plotted on a graph with a line connecting all the points, the y-intercept of the line represents _______ and the slope of the equation represents .

In this scenario, the y-intercept is________ .

fill in the blanks
here are the answer choices for the 1st one y=1.5x+80
y=0.

Answer 1

a) The slope of the line relating Alyssa's sales to earnings is given by 
   slope = (change in earnings)/(change in sales)
Using the first two table entries, the slope is calculated as
   slope = (110 -80)/(200 -10) = 30/200 = 0.15

The first entry in the table shows the y-intercept, the value of earnings (80) for zero sales. The slope-intercept form of the equation for a line is
   y = slope*x + y-intercept

To answer the first question, we put the slope and intercept values in the appropriate spots in the equation.

The equation that gives Alyssa's daily earnings based on her total sales is
   y = 0.15x +80

b) The y-intercept of the line represents the part of Alyssa's earnings that doesn't depend on sales. It is Alyssa's fixed daily wage.

c) The slope of the equation represents Alyssa's commission rate.

d) The y-intercept is 80.