Question 2.13: (a) A line passes through the points (2, 4) and (6, 1). Dedu......

(a) Step 1: The slope of the line is calculated by substituting the points into equation (2.8):

m={\frac{y_2  –  y_1}{x_{2} – x_{1}}}={\frac{1  –  4}{6  –  2}}={\frac{-3}{4}}=-0.75

Step 2: The equation of the line is deduced by substituting this slope, and either point, into equation (2.9)

y  −  y_1 = m(x  −  x_1)
y − 4 = −0.75(x − 2)       using point (2, 4)
y − 4 = −0.75x + 1.5
y = 5.5 − 0.75x

The equation of the line has a negative slope of −0.75 and y-intercept of 5.5.
(b) Following method A, use the equation of the line to calculate any three points as in Table 2.9. These points are then plotted in Figure 2.29.