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Understanding and Graphing Linear Functions: Finding Intercepts

This lesson covers the essentials of graphing linear functions and understanding intercepts. Learn how to identify x-intercepts and y-intercepts of linear equations, such as y = -x + 3 and y = 2x - 2. Gain insight into the significance of these intercepts in relation to the graph and how to calculate them through substitution. We will practice finding intercepts of various equations, sketching graphs, and interpreting the quantitative relationships they represent. Suitable for students to enhance their graphing and analytical skills.

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Understanding and Graphing Linear Functions: Finding Intercepts

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  1. Warm Up Graph the linear functions. 1. 2. y = -x + 3 y = 2x - 2

  2. INTERCEPTS OF GRAPHS

  3. 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)

  4. 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).

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

  6. Finding the intercepts • To find the x - interceptof a line, substitute y = 0 into the equation and solve for x. 2) To find the y - interceptof a line, substitute x = 0 into the equation and solve for y.

  7. Finding the x - interceptFind 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 0=2x -6 substitute 0 for y +6 +6 solve for x 6=2x 3=x Thus, the x-intercept is (3,0).

  8. Finding the y - interceptFind 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 = 2(0) -6 substitute 0 for x y = 0-6solve for y y = -6 Thus, the y- intercept is (0,-6).

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

  10. You tryFind the intercepts of the graph of y = -3x+6 • To find the x - intercept: Let y = 0 y = -3x+6 0=-3x +6 -6 -6 solve for x-6=-3x 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 = 0+6solve for y y = 6 Thus, the y -intercept is (0,6).

  11. Identify the intercepts 1) x - intercept: y - intercept: 3) x - intercept: y - intercept: -2 2) x - intercept: y - intercept: 4 2 -2 2 -1

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

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

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