Linear Functions.pptx Explanation of linear function

Linear functions

1. Linear Functions

2. Review If y is proportional to x , then When express y in terms of x , y = ? If y is inversely proportional to x , then When express y in terms of x , y = ?  

3. Review Coordinates P(2,3) X coordinate and Y coordinate Q (5, -4) R (-2,3) Graphing proportion and inverse proportion  

4. Linear Functions What is a linear function? It’s a function that can be represented as and are constants and How do we determine whether a function is linear or nonlinear?  

5. A linear equation in two variables , x and y , is an equation that can be written in the form , where a and b are constants (just numbers). Likewise, a linear function is a function whose graph is a non-vertical line. A linear function has a constant rate of change and can be represented by a linear equation in two variables. A nonlinear function does not have a constant rate of change and its graph is not a line.  

6. If you let be the total cost of a 40-yen bottle filled with grams of a drug costing 8-yen per gram, then (Total cost) = (Cost of drug) + (Cost of bottle), It takes seconds to run 400m at a speed of metres per second Time =   Examples

7. I n the rectangle on the right, Point P moves from B to C on side BC. Letting cm be the length of segment BP and cm 2 be the area of the DPC in terms of 2. Is a linear function of ? 3. Find value for y when = 0 and value of when = 12 4. Domain of x and domain of y (when point P is at vertices B and C)   Examples

8. Does the table represent a linear or nonlinear function? A linear function has a constant rate of change As x increases by 3, y decreases by 6. The rate of change is constant for both x and y . The function is linear. x 3 6 9 12 y 36 30 24 18 +3 +3 +3 -6 -6 -6

9. Does the table represent a linear or nonlinear function? A linear function has a constant rate of change As x increases by 2, y increases by different amounts. The rate of change is not constant for both x and y . The function is nonlinear. x 1 3 5 7 y 2 9 20 35 +2 +2 +2 +7 +11 +15

10. When the x value goes from 2 to 8 in the linear function , find increase in , increase in and the rate of change, I ncrease in is 8 – 2 = 6 Increase in Rate of change is   Examples

11. Does the graph represent a linear or nonlinear function? Explain. The function is linear. Because the graph is a line. The function is nonlinear. Because the graph is not a line.

12. Which of the following equations represent linear functions? Explain. A linear function can be written in the form , where m and b are constants (just numbers).   You cannot rewrite the equations , , , and in the form . So these equations cannot represent linear functions. You can rewrite the equation as You can rewrite the equation as So these equations represent linear functions.   , , , , , and  

13. Does the equation represent a linear or nonlinear function? Explain. A linear function can be written in the form .   You can rewrite the equation as Equation represents a linear function .     You can rewrite the equation as Equation represents a linear function .     You cannot rewrite the equation as Equation is a nonlinear function .    

14. Graphs of proportion & linear functions The graph of a linear function is a straight line formed by translating the graph of by the amount in the +ve direction along the y-axis.      

15. For the linear function , complete the table. Substitute each x and y value in the eqn using values.        

16. The graph of the linear function is a st line with a slope of a and b .   The slope is equal to Y intercept is equal to the constant -3.