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 scatter - plot, when \(x=0\) (years of experience = 0), the salary (in thousands) is around \(35\) (not \(40\)). So we can eliminate Line A (\(y=\frac{5}{6}x + 40\)) and Line C (\(y=\frac{6}{5}x+40\)) since their \(y\) - intercepts \(b = 40\) are not a good fit for the data near \(x = 0\).

Step2: Analyze the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Let's assume two points \((x_1,y_1)\) and \((x_2,y_2)\) from the scatter - plot. Suppose we take a point near the trend. For example, if we consider the general trend of the data. The slope of the line of best - fit should be such that for an increase in \(x\) (years of experience), the increase in \(y\) (salary) is moderate.
The slope of Line B is \(m=\frac{5}{6}\approx0.83\) and the slope of Line D is \(m = \frac{6}{5}=1.2\).
If we look at the rate of change of the data points (increase in salary with respect to years of experience), the slope \(\frac{5}{6}\) (Line B) is a more moderate increase compared to \(\frac{6}{5}\) (Line D) which would imply a steeper increase. The data points do not show such a steep increase.

Answer:

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