MATH 116 CONCEPTS WEEKS 2-4-6-8

# MATH 116 CONCEPTS - of a line is"the change in y divided by the change in x" Since x never changes the formula for finding the slope

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MATH 116 WEEK 2-4-6-8 CONCEPT CHECKPOINTS Week 2 Concept check 1) The system have ALL REAL SOLUTIONS, when the final step you got TRUE statement like this: 2x+3y =6 4x+6y =12 Solve this system. What is the solution of the system? We see if I times 2 both sides of first equation --> it become 4x+6y+12, so now i subtract this from second equation, I got 4x-4x +6y-6y = 12-12 0=0. TRUE STATEMENT. This is ALWAYS TRUE FOR ANY VALUE of X and Y. So we conclude: ALL REAL NUMBERS. 2) For no real solution, when final step we get FALSE STATEMENT 2x+4y=6 4x -8 = -8y find solution? Solve second equation : we have 4x -8 = -8y 4x +8y = 8 ( add 8 and add 8y both sides) Now times 2 both sides for first equation, I have 4x+8y = 12 We have a new system : 4x+8y = 12

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4x +8y = 8 Now subtract both sides 4x-4x+8y-8y = 12-8 =4 0=4 is a FALSE STATEMENT. So, FALSE STATEMENT, we conclude the system: NO REAL SOLUTION. Week 4 Concept Check On a Cartesian graph, x = 4 is a vertical line because the slope of the line is undefined. The slope
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Unformatted text preview: of a line is "the change in y divided by the change in x." Since x never changes, the formula for finding the slope results in a division by zero. All lines with an undefined slope are vertical lines. Week 6 concept check After putting the equations of two lines into the y = mx + b equation, the m represents the slopes of the lines. To determine if two lines are perpendicular, multiply their m values, or slopes, together and look at the product. If the product is anything else but -1, the lines are not perpendicular. Week 8 concept check The graph of the interval [-4,10] is a horizontal line with its left endpoint at -4 and its right endpoint at 10. The "[" indicates that -4 is included in the interval; we represent this by drawing a heavy dot at the left endpoint -4. The "]" indicates that 10 is included in the interval; we represent this by drawing a heavy dot at the right endpoint 10....
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## This note was uploaded on 04/09/2010 for the course MATH Math116 taught by Professor Na during the Winter '10 term at Phoenix School of Law.

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MATH 116 CONCEPTS - of a line is"the change in y divided by the change in x" Since x never changes the formula for finding the slope

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