Quantitative Analysis for Management, 13/e

M6.1 Slope of a Straight Line

Recall that the equation of a line can be written as

The equation of a straight line is Y$=$ a $+$ bX.

$$Y=a+bX$$ (M6-1)

where b is the slope of the line.

If we are given any two points $\left(X_1,Y_1\right)$ and $\left(X_2,Y_2\right),$ that are on a line, the slope is

$$b=\frac{\text{Change} \text{in}Y}{\text{Change} \text{in}X}=\frac{\Delta Y}{\Delta X}=\frac{Y_2-Y_1}{X_2-X_1}$$ (M6-2)

The slope of the line is the change in Y over the change in X.

where $\Delta$ (delta) is used to represent “change in.”

For example, the slope of the line that passes through the points (2,3) and (4,7) is

$$b=\frac{\Delta Y}{\Delta X}=\frac{7-3}{4-2}=\frac{4}{2}=2$$

We can find the intercept, a, by using this slope and either point in the equation for a line. For this example, if we select the point (2,3), we have

$$\begin{array}{lll}Y\hfill & =\hfill & a+bX\hfill \\ 3\hfill & =\hfill & a+2\left(2\right)\hfill \\ a\hfill & =\hfill & -1\hfill \end{array}$$

The equation of this line is then

$$Y=-1+2$$