graphoflinearequations-180821083542.pptx

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1. Graph of Linear Equations

2. Review How to determine the slope of a line?

3. How can you describe linear equations by graphing?

4. Graph of Linear Equations

5. Plot on a graph the points (2, 3) and (-1 ,-1)

6. Learning Competency Graph a linear equation given (a) any two points; (b) the x – and y – intercepts; (c) the slope and a point on the line. M8AL-If-2 Objectives: 1. Solve for the value of y in behalf of x 2. Graph the equation using any two points

7. Graph of Linear Equations L inear function can be described by its equation, either in the form y = mx + b or Ax + By = C. A linear equation can also be described by its graph. Graphing linear equations can be done using any of the four methods: Using any two points on the line Using x - and y -intercepts Using the slope and a point

8. Using Two Points on the line One method of graphing a linear equation is using two points. In Geometry, you learned that two points determine a line. Since the graph of the linear equation is a line, thus two points are enough to draw a graph of a linear equation.

9. Illustrative Example Graph the function y = 2 x + 1. You may assign any two values for x , say 0 and 1. By substitution, y = 2 x + 1 y = 2 x + 1 y = 2(0) + 1 y = 2(1) + 1 y = 0 + 1 y = 2 + 1 y = 1 y = 3 If x = 0, then y = 1. Furthermore, if x = 1, then y = 3. So, the ordered pairs are (0, 1) and (1, 3). This means that the line passes through these points.

10. After finding the ordered pairs of the two points, plot and connect them. Your output is the graph of the linear equation.

11. Exercise 8 Graph each linear equation that passes through the given pair of points. ( 1, 2) and (3, 4) (5 , 6) and (0, 11) (-2, ) and ( , - ) (- , - ) and ( , )  

12. Answers 1. 3. 2. 4.

13. Using x -Intercept and y -Intercept Secondly, the linear equation can be graphed by using x -intercept a and y -intercept b . The x - and y -intercepts of the line could represent two points, which are ( a , 0) and (0, b ). Thus, the intercepts are enough to graph the linear equation.

14. Illustrative Example To graph the equation y = 2 x + 1 using this method, you need to solve the x -intercept by letting y = 0 and the y -intercept by letting x = 0. Letting y = 0, the equation y = 2 x + 1 becomes = 2 x + 1 Substitution - 2 x = 1 Addition Property of Equality x = -12 Multiplication Property of Equality Letting x = 0, y = 2 x + 1 becomes y = 2(0) + 1 Substitution y = 0 + 1 Simplification y = 1 Simplification The x -intercept a is -12 while the y -intercept b is 1.

15. Now, plot the x - and y -intercepts, then connect them. The x- intercept is the abscissa of the coordinates of the point in which the graph intersects the x- axis . However, the y- intercept is the ordinate of the coordinates of the point in which the graph intersects the y- axis .

16. Exercise 9 Graph each linear equation whose x -intercept a and y -intercept b are given below. 1. a = 2 and b = 1 2. a = 4 and b = -1 3 . a = -2 and b = -7 4 . a = and b = -2  

17. Answers 1. 3. 2. 4.

18. Using Slope and a Point The third method in graphing linear equation is by using the slope and one point. This can be done by plotting first the given point, then finding the other point using the slope.

19. The linear equation y = 2 x + 1 has a slope of 2 and a point (-1, -1). To find a point from this equation, we may assign any value for x in the given equation. Let’s say, x = -1. The value of y could be computed in the following manner:

20. Exercise 11 Graph the following equations given slope m and a point. 1. m = 3 and (0, -6 ) 2. m = -2 and (2, 4) 3. m = and (0, 4) 4 . m = and (2, -3)  

21. Answers 1. 2.

22. Answers 3. 4 .

23. Group Board Work Contest The class will be divided into 4 groups. In every problem given, 2 representative of the group can go to the board and write the answer/solutions on the board. The first group to answer correctly will receive the point.

24. How important is graphing in real life situations ?

25. Generalization The graph of a linear equation can be drawn in the coordinate plane using any two points, the x- and y- intercepts of the line, slope and y-intercept and using slope and one point. Graphing is a clear representation of data which could easily be understood.

26. Additional Activity: Write the Steps Description: This activity will enable you to summarize the methods of graphing a linear equation. Direction: Fill in the diagram below by writing the steps in graphing a linear equation using 4 different methods.

27. Thank you for your cooperation! Janette M. Basco , SST-I San Vicente National High School