Ex 2.6, 1 (ii)

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Ex 2.6, 1 (ii) Draw the graphs of the following sets of lines. In each case, reflect on the role of ‘a’ and ‘b’. (ii) y = – 6x, y = – 3x, y = – x To draw the graph, we join points which lie on the line For y = –6x Putting x = 0 y = –6 × 0 y = 0 So, x = 0, y = 0 lie on the line i.e. (0, 0) lies on the line Putting x = 1 y = –6 × 1 y = –6 So, x = 1, y = –6 lie on the line i.e. (1, –6) lies on the line For y = –x Putting x = 0 y = –0 y = 0 So, x = 0, y = 0 lie on the line i.e. (0, 0) lies on the line Putting x = 1 y = –1 So, x = 1, y = –1 lie on the line i.e. (1, –1) lies on the line For y = –3x Putting x = 0 y = –3 × 0 y = 0 So, x = 0, y = 0 lie on the line i.e. (0, 0) lies on the line Putting x = 1 y = –3 × 1 y = –3 So, x = 1, y = –3 lie on the line i.e. (1, –3) lies on the line y = –6x y = –x y = –3x Reflection on 'a' and 'b’ Because b = 0, all three of these lines will cross exactly through the center origin point (0, 0). Because the 'a' values are negative, they all travel ”downhill" from left to right. As the negative number gets larger (further from zero), the downhill drop becomes much steeper. The line y = -6x is the steepest drop.