Question

1. the graph to the right shows the salary each employee at a company along with their years of experience. which line best represents this data?

line a: ( y=\frac{5}{6}x + 40 )
line b: ( y=\frac{5}{6}x + 35 )
line c: ( y=\frac{6}{5}x + 40 )
line d: ( y=\frac{6}{5}x + 35 )

Explanation:

Step1: Analyze the y - intercept

The y - intercept of a line \(y = mx + b\) is the value of \(y\) when \(x = 0\). Looking at the data points, when \(x=0\) (years of experience = 0), the salary is close to \(35\) (in thousands). So \(b\approx35\).

Step2: Analyze the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Let's take two points. Suppose we consider a point where \(x = 6\) and \(y\approx40\) and another point where \(x=12\) and \(y\approx45\). Then \(m=\frac{45 - 40}{12 - 6}=\frac{5}{6}\)

Answer:

Line B: \(y=\frac{5}{6}x + 35\)