Warm Up 0?1? 2? Graph the linear functions.0?1? 2?

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Presentation transcript:

Warm Up 0?1? 2? Graph the linear functions.0?1? 2?

INTERCEPTS OF GRAPHS

Objectives  Graph and interpret linear Functions. (AF 3.0)  Represent quantitative relationships graphically and interpret the meaning of a specific part of the graph in the situation represented by the graph. (AF 1.5)

INTERCEPTS OF A GRAPH Intercepts- points at which the graph intersects the x- or y-axis. What number do the x- and y- intercepts have in common? Finding intercepts:  An x-intercept is written as the ordered pair (x, 0).  A y-intercept is written as the ordered pair (0, y).

 The graph of any linear equation in two variables is a straight line. y x Intercepts Finding intercepts can be helpful when graphing. The x-intercept is the point where the line crosses the x-axis. The y-intercept is the point where the line crosses the y-axis. x - intercept y - intercept

Finding the intercepts 1)To find the x - intercept of a line, substitute y = 0 into the equation and solve for x. y = 0 into the equation and solve for x. 2) To find the y - intercept of a line, substitute x = 0 into the equation and solve for y. x = 0 into the equation and solve for y.

Finding the x - intercept Find the x-intercept of the graph of the equation y =2x-6  To find the x-intercept: substitute in ZERO for y and solve for y. y = 2x-6 write the equation y = 2x-6 write the equation 0=2x -6 substitute 0 for y 0=2x -6 substitute 0 for y solve for x solve for x 6=2x 6=2x 3=x 3=x Thus, the x-intercept is (3,0).

Finding the y - intercept Find the y-intercept of the graph of the equation y =2x-6  To find the y-intercept: substitute in ZERO for x and solve for y. y = 2x-6 write the equation y = 2x-6 write the equation y = 2(0) -6 substitute 0 for x y = 2(0) -6 substitute 0 for x y = 0-6 solve for y y = 0-6 solve for y y = -6 y = -6 Thus, the y- intercept is (0,-6).

Find the intercepts of y = 4x+4  To find the x - intercept: Let y = 0 y = 4x+4 y = 4x+4 0=4x +4 0=4x solve for x -4=4x solve for x -4=4x -1 = x -1 = x Thus, the x-intercept is (-1,0).  To find the y - intercept: let x=0 y = 4x+4 y = 4(0) +4 y = 4x+4 y = 4(0) +4 y = 0+4 solve for y y = 0+4 solve for y y = 4 y = 4 Thus, the y -intercept is (0,4).

You try Find the intercepts of the graph of y = -3x+6  To find the x - intercept: Let y = 0 y = -3x+6 y = -3x+6 0=-3x +6 0=-3x solve for x -6=-3x solve for x -6=-3x 2= x 2= x Thus, the x-intercept is (2,0).  To find the y - intercept: let x=0 y = -3x+6 y = -3(0) +6 y = -3x+6 y = -3(0) +6 y = 0+6 solve for y y = 0+6 solve for y y = 6 y = 6 Thus, the y -intercept is (0,6).

Identify the intercepts 1) x - intercept: y - intercept: y - intercept: 2) x - intercept: y - intercept: y - intercept: 3) x - intercept: y - intercept: y - intercept:

Sketch a graph using the intercepts x - intercept: 4 y - intercept: 3

Sketch a graph using the intercepts 1) x - intercept: -2 y - intercept: 3 y - intercept: 3 2) x - intercept: 2 y - intercept: 4 y - intercept: 4 3) x - intercept:-3 y - intercept:-4 y - intercept:-4