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Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function Chart A: The parent function of a linear relationship is y = x. If a coefficient is placed in front of the x, it causes the steepness or slope of the graph to be changed. Use the graphing calculator to investigate and describe the changes in steepness “m” has on the graph of the linear parent function y = x. Function Value of “m” in y = mx Up or down from left to right? Is the steepness more, less, or the same as y = x? x 1 Up Same x -1 Sketch (both parent function and given function on each coordinate plane) When x increases Coordinates by 1, y of the (increases, y-intercept decreases) by ____ y 10 8 6 4 y=x 2 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 -2 Increases by 1 (0, 0) -4 -6 -8 -10 y 10 8 6 4 y x 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10 y 10 8 6 4 Increases by 2 2 y = 2x -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 y 10 8 6 4 2 y = 0.5x -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 ©2012, TESCCC 07/12/12 page 1 of 7 Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function Function Value of “m” in y = mx Sketch Up or down from left to right? Is the steepness more, less, or the same as y = x? When x increases Coordinates by 1, y of the (increases, y-intercept decreases) by ____ y 10 8 6 4 y 0.5 x 2 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 x Down -2 -4 -6 -8 -10 y 10 8 6 4 2 y = 3.5x -10 -8 -6 -4 -2 (0, 0) x -2 -4 -6 -8 -10 y 10 8 6 4 y 3.5 x 2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 y 10 8 6 Increases 4 by 3 4 4 y= x 3 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8 -10 ©2012, TESCCC 07/12/12 page 2 of 7 Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function Function Value of “m” in y = mx Sketch Up or down from left to right? Is the steepness more, less, or the same as y = x? When x increases Coordinates by 1, y of the (increases, y-intercept decreases) by ____ y 10 8 6 4 1 y x 3 2 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 x -2 -4 -6 -8 -10 y 10 8 6 4 1 y= x 4 2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 y 10 8 6 4 y 1.5 x 2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 ©2012, TESCCC 07/12/12 page 3 of 7 Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function Use the information from Chart A to help you answer the following: 1. When “m” is positive, does the line go up or down from left to right? __________ 2. When “m” is negative, the line goes ______________ from left to right. 3. When the line is less steep than the graph of y = x what is true about the value of “m”? 4. Does changing the value of “m” cause the line to curve or become a figure other than a line? 5. Does changing the value of “m” change where the line intersects the y-axis? What is the point of intersection? 6. Predict the graph of y = -5x. Sketch your prediction. Remember to label the x-axis and y-axis. 7. How do you know from the graph if the measure of steepness is positive or negative? ©2012, TESCCC 07/12/12 page 4 of 7 Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function Chart B: The parent function of a linear relationship is y = x. If a number is added to or subtracted from x, it changes the position of the line with respect to the x and y axes. Use the graphing calculator to investigate and describe the effect the addition or subtraction of a “b” value has on the location of the graph of the linear parent function y = x. Function Value of “m” in y = mx Sketch Point of intersection on y-axis Up or down from left to right? Is the line more, less, or the same steepness? y 10 8 6 4 y=x 2 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 x -2 -4 -6 -8 -10 y 10 8 6 4 2 y = x+2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 y 10 8 6 4 y=x–2 2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 y 10 8 6 4 y=x–5 2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 ©2012, TESCCC 07/12/12 page 5 of 7 Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function Function Value of “m” in y = mx Sketch Point of intersection on y-axis Up or down from left to right? Is the line more, less, or the same steepness? y 10 8 6 4 1 y =x+ 2 2 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 x -2 -4 -6 -8 -10 y 10 8 6 4 2 y = x +5 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 y 10 8 6 y x 1 2 4 2 -10 -8 -6 -4 -2 x -2 -4 -6 -8 -10 Use the information from Chart B to help you answer the following: 8. Does addition or subtraction of a value of “b” change where the line intercepts the y-axis? Explain these changes. 9. Does addition or subtraction of a value of “b” change whether the line goes up or down from left to right? 10. Does addition or subtraction of a value of “b” change the steepness of the line? ©2012, TESCCC 07/12/12 page 6 of 7 Algebra 1 HS Mathematics Unit: 04 Lesson: 01 Parameter Changes on the Linear Parent Function 11. Does addition or subtraction of a value of “b” cause the line to curve or become a figure other than a line? 12. Predict the graph of y = x + 6. Sketch your prediction. Remember to label the x-axis and y-axis. ©2012, TESCCC 07/12/12 page 7 of 7