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Graphing straight lines The gradient-intercept form of a straight line is: y = mx + b wherem is the gradient andb is the y-intercept. If the line is not in this form, I would change it to this form. How I use this form to plot a line: Plot the y-intercept (b) Move up by the “rise” Move across by the “run” Plot the 2 nd point Join the two points to form the line. Alternate method Complete a table of values Use at least three values.

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Example 1 Graph the line y = 2x + 1 Method 1 Plot the point (0, 1) As the gradient is 2, this is 2 / 1. Move up by 2 Move across 1 Plot the 2 nd point Join the two points to form the line. Method 2 Complete a table of values Use at least three values. y = 2x + 1 x y –11 01 3

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Example 2 Graph the line 3x + 2y + 4 = 0 Method 1 Change to y = mx + b 3x + 2y + 4 = 0 2y = –3x – 4 y = –3x / 2 – 2 Plot the point (0, –2) Move down by 3, as the gradient is negative Move across 2 Plot the 2 nd point Join the two points to form the line. Method 2 Change to y = mx + b y = –3x / 2 – 2 Pick “nice” values for x. Multiples of 2, as the denominator is 2 x y 1–2 02 –5 –2

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Graphing straight lines Lines parallel to the axes The line x = a is parallel to the y-axis, the y-values change but x always equals a. Example 3 Graph the line x = 3 The line y = b is parallel to the x-axis, the x-values change but y always equals b. Example 4 Graph the line y = –2

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Does a point lie on the line? A point lies on a line if its coordinates satisfy the equation of the line. OR Substitute the point into the equation of the line; if LHS = RHS, the point lies on the line. if LHS ≠ RHS, the point is not on the line Example 6 Does the point line 3x + 2y – 22 = 0 pass through the point (4, 5)? 3(4) + 2(5) – 22 = 0 0 = 0 The line 3x+2y–22 = 0 passes through the point (4, 5). Example 5 Does the point (2, 5) lie on the line y = 3x + 1? 5 = 3(2) + 1 5 ≠ 7 (2, 5) IS NOT on the line y = 3x + 1.

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Today’s work Yesterday’s work Exercise 10:05 Q1-4 Exercise 8:03 Q1 a, c, e…o, p, q & r, Q2 & 3 all

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