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# February 11, 2014

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### February 11, 2014

1. 1. February11, 2014 Today Review: Parallel/Perpendicular Lines, Inequalities Complete Class Work from Friday/Monday Thank You Khan Academy People; Lot's of Work, Nicely Done
2. 2. Parallel & Perpendicular Lines
3. 3. Parallel Lines Have the Same Slope • The lines never touch. Therefore: • There is no solution to a system of equations • If you know the slope of one line, you know the slope of a line parallel to it. • If you know the slope and a point on the line, you can use the point-slope formula to find the equation of, and graph the line.
4. 4. The question says: The equation of a line parallel to the one shown could be; It doesn’t matter what points the line goes through, as long as the slope is the same Find the slope.. Which is the equation of a line parallel to all those shown on the graph? A) y = 3x – 7 B) y < 3x – 7 C) 4x +2y = -11 D) 3x –y = 4
5. 5. Write the equation and graph the line parallel to the one shown and passing through the point (3,-4). Whole different story, this one. The line must pass thru Again, find the slope of the current line, then use the pointslope formula to find the new equation. Point-Slope: Y + 4 = -3(x – 3) Equation: Y = -3x + 5
6. 6. Parallel Lines An equation of a line parallel to the graph could be: A. y = -4/3x + 3 B. y = 4/3x -2 C. y = -3/4x + 2 D. y = -4x -3 E. None
7. 7. Parallel Lines What is the equation of the line parallel to the line 2y –x = 1, and passing thru the point (-4,5) A. y = -x + 5/2 B. y = 2x – 5/2 C. y = -1/2x + 5 D. y = 1/2x – 5 E. None
8. 8. Perpendicular Lines Have Slopes that are the opposite inverse of each other • The lines cross at a 90 degree angle • There is always one solution • If you know the slope of one line, change the sign and use the reciprocal • If you know the slope and a point on the line, you can use the point-slope formula to find the equation of, and graph the line.
9. 9. Write the equation of the line perpendicular to the one shown passing through the point (3,-4). Again, find the slope of the current line, then use the pointslope formula to find the new equation.
10. 10. Inequaliti es: Which inequality is shown on the graph? A. y < 2x – 1 B. C. y > -2x - 1 D. E.
11. 11. Inequaliti es: Which graph represents the inequality 6y – 8x < -24
12. 12. Systems of Equations
13. 13. Testing A Specific Ordered Pair for Solution: 1. Change the inequality to an equation 2. Solve as system of equations ( elimination or substitution) 3. Replace = sign with original inequality signs and test point
14. 14. Solving a 3x3 System of Equations The sum of three numbers is 14. The largest is 4 times the smallest. The sum of the smallest and two times the largest is 18. Find the numbers. ( In the form, (largest, middle, smallest number) ).
15. 15. Applying Systems of Equations Example • A pizza parlor charges \$1 for each veggie topping and \$2 for each meat topping. You want at least five toppings on your pizza. You have \$10 to spend on toppings. How many of each topping can you get on your pizza? ì x + 2y £10 í îx + y ³ 5