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M. Pickens 2006 Intercepts

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M. Pickens 2006 Objectives To learn what intercepts are To learn how to find x and y-intercepts of a graph To learn how to find x and y-intercepts of an equation To use x and y-intercepts to sketch a graph

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M. Pickens 2006 What are intercepts? An intercept is where something intersects or crosses For example, an x-intercept is where a line crosses the x-axis a y-intercept is where a line crosses the y- axis

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M. Pickens 2006 Intercepts of a Graph What are the x- intercept and y- intercept of the graph at right? X-intercept: Y-intercept: Where it touches the x-axis x (5, 0) Where it crosses the y-axis y (0, 7)

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M. Pickens 2006 Intercepts of a Graph What are the x- intercept and y- intercept of the graph at right? X-intercept: Y-intercept: Where it touches the x-axis x (-8, 0) Where it crosses the y-axis y (0, 6)

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M. Pickens 2006 Intercepts of a Graph What are the x and y-intercepts of the graphs below? X-intercept: Y-intercept: X-intercept: Y-intercept: (3, 0) (0, -8) (-9, 0) (0, -5) Notice: For all the x-intercepts the y-coordinate is ____ For all the y-intercepts the x-coordinate is ____ 0 0

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M. Pickens 2006 Which are which? Which of the coordinates below are x-intercepts? Which of the coordinates below are y-intercepts? R(3, 5)S(0, 9)T(-2, 0)U(0, 1)V(15, 0) W(0, 0) X( ½, 0) Y(0, 8)Z(1, 0.5) T, V, W, X S, U, W, Y

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M. Pickens 2006 Intercepts of an Equation We know for an x-intercept the ______________ is 0 In the y-intercept the ___________ is 0 We can use this to solve equations. To solve for an x-intercept plug in a 0 for y. To solve for a y-intercept plug in a 0 for x. Y-coordinate x-coordinate

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M. Pickens 2006 Intercepts of an Equation Find the x and y-intercepts of the equation -2x + 3y = 19 To find the x-intercept plug in 0 for _____ y -2x + 3y = 19 -2x + 3(0) = 19 -2x + 0 = 19 -2x = 19 -2 x = -9.5( -9.5, 0) To find the y-intercept plug in 0 for _____ x -2x + 3y = 19 -2(0) + 3y = 19 0 + 3y = 19 3y = 19 3 y = 6.3( 0, 6.3)

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M. Pickens 2006 Intercepts of an Equation Find the x and y-intercepts of the equation To find the x-intercept plug in 0 for _____ y - 16 -16 5* *5 -80=-4x x = 20(20, 0) To find the y-intercept plug in 0 for _____ x y = 16(0, 16)

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M. Pickens 2006 Sketching a Graph from Intercepts Find the intercept of the equation 3x + y =12 and sketch the graph X-intercept: (Plug in 0 for y) 3x + 0 = 12 3x = 12 x = 4 (4, 0) Y-intercept: (Plug in 0 for x) 3(0) + y = 12 0 + y = 12 y = 12 (0, 12)

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M. Pickens 2006 Sketching a Graph from Intercepts Find the intercept of the equation and sketch the graph X-intercept: (Plug in 0 for y) x = 6 (6, 0) Y-intercept: (Plug in 0 for x) y = 0 – 3 y = -3 (0, -3) + 3 +3 2* *2

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M. Pickens 2006 Conclusion Intercept is : _____________________ The x-intercept is _________________ The y-intercept is _________________ To find the x-intercept of an equation ____________________ To find the y-intercept of an equation ____________________ Where something intersects or touches Where a line crosses the x-axis Where a line crosses the y-axis Plug in 0 for Y Plug in 0 for X

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Example 1 Find the intercepts of the graph of. Finding Intercepts 2 1 y = x – 5 2 1 0 = x – 5 2 1 5 = x 10 = x STEP 1 Let 0 and solve for x to find the.

Example 1 Find the intercepts of the graph of. Finding Intercepts 2 1 y = x – 5 2 1 0 = x – 5 2 1 5 = x 10 = x STEP 1 Let 0 and solve for x to find the.

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