Question 2.12: (a) Deduce the equation of a line whose slope is of 1.7 and ......

Essential Mathematics for Economics and Business [1390651]

(a) Deduce the equation of a line whose slope is of 1.7 and which passes through the point (2, 5).
(b) Plot the graph of the line.

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(a) Using equation (2.9), the equation of the line is deduced as

$y - y_1 = m(x - x_1)$
y − 5 = 1.7(x − 2)
y − 5 = 1.7x − 3.4
y = 1.6 + 1.7x

This line has a slope of 1.7 and it intersects the y-axis at y = 1.6.

(b) To plot the line it is necessary to calculate at least two points on the line; however, it is a good idea to calculate three points in case of error. All three points should lie exactly on the line. Using method A, take suitable x-values and calculate the corresponding y-coordinates from the equation of the line as shown in Table 2.8. These points are plotted in Figure 2.28.

Table 2.8 Calculating points on the line, y = 1.6 + 1.7x
x	y= 1.6 + 1.7x	Point (x, y)
-2	y = 1.6 + 1.7(−2)=−1.8	(−2, −1.8)
0	y = 1.6 + 1.7(0) = 1.6	(0, 1.6)
2	y = 1.6 + 1.7(2) = 5	(2, 5)

2.28a

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