# graphing linear functions graphing straight lines this presentation looks at two methods for...

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GRAPHING LINEAR FUNCTIONS

Graphing Straight LinesThis presentation looks at two methods for graphing a line.1.By finding and plotting points2.Using the gradient and the y-intercept where y = mx + b

1.Graphing Straight Lines by plotting pointsy = 2x 1Choose values for x and find the corresponding value for yx = 1, y = 2(1) - 1 = 1x = 2, y = 2(2) - 1 = 3x = -1, y = 2(-1) - 1 = - 3Connect the pointsThis information is often presented in table formx

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

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

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

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

2.Graphing Straight Lines by using the gradient and the y-interceptm = y-intercept = 2Place a point at the y-interceptThis gives us the point (3, 4) Connect the points

Re-arranging equations to read the gradient and the y-interceptRemember the general form of a straight line is y = mx + b Example 1Subtract x from both sidesRearrange so that the x term is firstTherefore, the gradient is 1 and the y-intercept is 7.

y = mx + b Example 2Subtract 3x from both sidesRearrange so that the x term is firstTherefore, the gradient is 3 and the y-intercept is 2

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

y = mx + b Example 4Add x to both sidesRearrange so that the x term is firstDivide both sides by 2

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

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

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