A, B, C are Notes Lesson 3 4 Standard Form of an Equation: Integers Ax + By = C Sometimes it is preferred that A is Positive All lines in the plane can be written in standard form. Oblique Coordinate Horizontal Only and lines can be written in slope intercept form. Jul 8 9:35 PM 1
1. What is the Standard Form for the equation of a linear function? 2. What do we know about the values of A, B, and C in the Standard Form? Ax + By = C where A and B are not both equal to zero. Standard Form will be easier to work with if A, B, and C are integers and A is positive. 3. What is the graph of the equation Ax + By = C when A and B are not both zero? A line 4. The slope of a line in Standard Form Ax + By = C is equal to what fraction? The slope of a line in Standard Form is where B does not equal zero and A and B can be positive or negative. 5. How can we find the y intercept of a line when it is written in standard form? 6. What kind of line do we end up with if A = 0? The y intercept of a line in Standard Form is where B does not equal zero and C and B can be positive or negative. Ax + By = C 0x + By = C By = C > a horizontal line 7. Give the equation and type of line when B = 0. Ax + By = C Ax + 0y = C Ax = C > a vertical line Sep 29 9:31 PM 2
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10. What is the slope of any vertical line? 11. Summarize the three types of lines. Undefined 12. Which lines are graphs of functions? 13. When graphing an equation in standard form it is easier to find the x intercept and y intercept. How do we find the y intercept? How do we find the x intercept? Oblique and horizontal lines are graphs of functions? Substitute zero for x and solve for y = Substitute zero for y and solve for 14. What is a y intercept? 15. What is an x intercept? It is a point where a graph crosses the y axis and can be found by substituting zero for x It is a point where a graph crosses the x axis and can be found by substituting zero for y Sep 29 9:33 PM 4
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Graph Using a Table 4x + 9y = 27 Find 2 points, other than the x and y intercept, that are on the line. Graph Using Slope Intercept Form 14x 7y = 21 Rewrite the equation in slope intercept form. Graph Using Intercept Method 3x 5y = 15 Find the x and y intercepts x y Aug 3 9:13 AM 6
Graph 1 Graph 2 Graph 3 Domain Range Aug 3 10:02 AM 7
Determine whether each line is oblique, horizontal, or vertical. A) 12 y = 18 B) 6x + 8y = 36 C) 7x = 21 Jul 8 9:54 PM 8
Use your hand to signal after each roll. Determine if the line is: 1. Horizontal 2. Vertical 3. Oblique Oct 17 7:14 AM 9
Domain: Range: Function: Range: Domain: Function: Aug 5 7:18 AM 10
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Relation Domain Range 7. 8. 9. x = 12 Function? Explain 10. y = 7 11. 12. 13. 14. 15. 16. 17. 18. Aug 5 7:26 AM 13
Rewrite each equation below in standard form Determine if the equation represents a vertical, horizontal or oblique line 19. 2 y = 3x 7 3 20. 7x + 15 = 3x 9y oblique line vertical line horizontal linoblique line vertical line horizontal line 21. 5x 3 = 5x 10y 22. 5y x = 19 + x + 5y oblique line vertical line horizontal line 23. 1y = 3x 2 5 2 oblique line vertical line horizontal line 24..25x +.6y = 1.5 oblique line vertical line horizontal line oblique line vertical line horizontal line Aug 5 7:30 AM 14
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