Question

thomas is a car salesman. the table shows the monthly salary that thomas earns for the number of cars he sells. use the data to graph the linear function. write the equation of the line, identify the slope of the line and explain what the slope means.

Explanation:

Step1: Find the slope

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,2000)\) and \((x_2,y_2)=(1,2300)\). Then \(m=\frac{2300 - 2000}{1-0}=300\).

Step2: Write the equation of the line

The slope - intercept form of a line is \(y = mx + b\). When \(x = 0\), \(y=b\). From the table, when \(x = 0\) (number of cars sold), \(y = 2000\) (monthly salary), so \(b = 2000\). The equation is \(y=300x + 2000\).

Step3: Interpret the slope

The slope \(m = 300\). In the context of the problem, \(x\) is the number of cars sold and \(y\) is the monthly salary. The slope means that for each additional car Thomas sells, his monthly salary increases by $300.

Answer:

The equation of the line is \(y = 300x+2000\). The slope of the line is \(300\). The slope means that for every car Thomas sells, he earns an additional $300.