Ex 2.6, 1 (v)

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Ex 2.6, 1 (v) Draw the graphs of the following sets of lines. In each case, reflect on the role of ‘a’ and ‘b’. (v) y = –2x – 3, y = –2x, y = 2x + 3 There is a typo here, 3rd line is y = –2x + 3 For y = –2x – 3 Putting x = 0 y = –2 × 0 – 3 y = 0 – 3 y = –3 So, x = 0, y = –3 lie on the line i.e. (0, 0) lies on the line Putting x = 1 y = –2 × 1 – 3 y = – 2 – 3 y = –5 So, x = 1, y = –5 lie on the line i.e. (1, –5) lies on the line For y = –2x Putting x = 0 y = –2 × 0 y = 0 So, x = 0, y = 0 lie on the line i.e. (0, 0) lies on the line Putting x = 1 y = –2 × 1 y = –2 So, x = 1, y = –2 lie on the line i.e. (1, –2) lies on the line For y = –2x + 3 Putting x = 0 y = –2 × 0 + 3 y = 0 + 3 y = –3 So, x = 0, y = 3 lie on the line i.e. (0, 3) lies on the line Putting x = 1 y = –2 × 1 + 3 y = – 2 + 3 y = 1 So, x = 1, y = 1 lie on the line i.e. (1, 1) lies on the line y = –2x – 3 y = –2x y = –2x + 3 Reflection on 'a' and ‘b’ Because the slope 'a' is exactly the exact same for all three lines (-2), they all have the exact same "downhill" steepness. Because they have the same steepness, they are perfectly parallel lines—they will never, ever intersect! The 'b' values tell us how these parallel lines are stacked. The middle line (y = -2x) goes straight through the origin (0,0). The line y = -2x + 3 is that exact same line, just shifted straight up like an elevator by 3 units. The line y = -2x - 3 is shifted straight down by 3 units.