Michael's total weekly pay includes a base salary plus certain percent of his sales. The table below show Michael's sales for 4 weeks and his total weekly pay. This data represents a linear function. What is Michael's weekly base salary?
Sales (x)week 1: $800 week 2: $460 week3: $540 week 4: $1000 Total Pay(y) week 1:$560 week 2: $460 week 3: $540 week 4: $600
A linear equation is y=mx+b where x is the sales, b is the base pay, and m is the percentage used to find the commission. We have
560 = m*800 + b
460 = m*460 + b
540 = m*540 + b
600 = m*1000 + b
Those points do not fit any linear equation. Check for typos.
Sorry Steve, I miscopied the data, the x values for weeks 2 and 3 week 2 is actually 300 on sales and week 3 is 700 on sales, my bad
Seth took a math quiz last week. There were 70 problems on the quiz and Seth answered 90% of them correctly. How many problems did Seth get correct?
To find Michael's weekly base salary, we need to determine the constant rate at which his pay increases or decreases as a result of his sales. Since the relationship between sales and pay is linear, we can find this constant rate by calculating the slope of the line that represents the data.
To calculate the slope, we can use the formula:
slope = (change in y) / (change in x)
The "change in y" represents the difference in the values of the dependent variable (total pay) between two points, and the "change in x" represents the difference in the values of the independent variable (sales) between the same two points.
Let's calculate the slope using the data given:
Slope between week 1 and week 2:
slope = (460 - 560) / (460 - 800)
slope = -100 / -340
slope = 0.2941
Slope between week 2 and week 3:
slope = (540 - 460) / (540 - 460)
slope = 80 / 80
slope = 1
Slope between week 3 and week 4:
slope = (600 - 540) / (1000 - 540)
slope = 60 / 460
slope = 0.1304
Since the slope represents the change in y (total pay) per unit change in x (sales), we can deduce that Michael's pay increases by $0.2941 for each dollar increase in sales.
To find Michael's weekly base salary, we need to identify the total pay when the sales are zero. By substituting any of the points into the equation, we will be able to determine the y-intercept, which corresponds to the base salary.
Using the week 1 data point (x = 800, y = 560):
560 = (0.2941 * 800) + b
560 = 235.28 + b
b = 560 - 235.28
b = 324.72
Therefore, Michael's weekly base salary is $324.72.