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Intercepts

Intercepts. 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. What are intercepts?. An intercept is where something intersects or touches

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Intercepts

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  1. Intercepts

  2. 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

  3. What are intercepts? • An intercept is where something intersects or touches • For example, • an x-intercept is where it touches the x-axis • a y-intercept is where it touches the y-axis

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

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

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

  7. Which are which? • Which of the coordinates below are x-intercepts? • Which of the coordinates below are y-intercepts? T, V, W, X S, U, W, Y 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)

  8. 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

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

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

  11. 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 (4, 0) x = 4 Y-intercept: (Plug in 0 for x) 3(0) + y = 12 0 + y = 12 (0, 12) y = 12

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

  13. Conclusion Where something intersects or touches • 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 it touches the x-axis Where it touches the y-axis Plug in 0 for Y Plug in 0 for X

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