GRAPHING LINEAR FUNCTIONS

Graphing Straight Lines This presentation looks at two methods for graphing a line. 1.By finding and plotting points 2.Using the gradient and the y - intercept where y = mx + b m is the gradient b is the y-intercept

1.Graphing Straight Lines by plotting points y = 2x – 1 Choose values for x and find the corresponding value for y x = 1, y = 2(1) - 1 = 1 x = 2, y = 2(2) - 1 = 3 x = -1, y = 2(-1) - 1 = - 3 Connect the points This information is often presented in table form x y –1 –3

y = – x + 2 Choose values for x and find the corresponding value for y x = 1, y = -(1) +2 = 1 x = 2, y = -(2) +2 = 0 x = -1, y = -(-1) +2 = 3 x = 3, y = -(3) +2 = -1 Connect the points 1.Graphing Straight Lines by plotting points

2.Graphing Straight Lines by using the gradient and the y -intercept y = 2 x – 3 m = y- intercept = 2 – 3 Place a point at the y -intercept A gradient of 2 is a rise of 2 over a run of 1 This gives us the point (1, –1) Connect the points

2.Graphing Straight Lines by using the gradient and the y -intercept y = – 4 x + 2 m = y- intercept = – 4 2 Place a point at the y -intercept A gradient of –4 is a drop of 4 over a run of 1 This gives us the point (1, –2) Connect the points

2.Graphing Straight Lines by using the gradient and the y -intercept y = – x – 3 m = y- intercept = – 1 – 3 Place a point at the y -intercept A gradient of –1 is a drop of 1 over a run of 1 This gives us the point (1, –4) Connect the points

2.Graphing Straight Lines by using the gradient and the y -intercept m = y- intercept = 2 Place a point at the y -intercept This gives us the point (3, 4) Connect the points A gradient of is a rise of 2 over a run of 3

Re-arranging equations to read the gradient and the y -intercept Remember the general form of a straight line is y = mx + b Example 1 Subtract x from both sides Rearrange so that the x term is first Therefore, the gradient is – 1 and the y -intercept is 7.

y = mx + b Example 2 Subtract 3 x from both sides Rearrange so that the x term is first Therefore, the gradient is – 3 and the y -intercept is – 2

y = mx + b Example 3 Subtract 4 x from both sides Rearrange so that the x term is first Therefore, the gradient is 4 and the y -intercept is – 1 Multiply both sides by – 1

y = mx + b Example 4 Add x to both sides Rearrange so that the x term is first Divide both sides by 2 Therefore, the gradient is and the y -intercept is 2.5

y = mx + b Example 5 Add 2 x to both sides Rearrange so that the x term is first Divide both sides by 3 Therefore, the gradient is and the y -intercept is

y = mx + b Example 6 Subtract 4 x from both sides Rearrange so that the x term is first Divide both sides by 2 Therefore, the gradient is – 2 and the y -intercept is 3

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