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Name:________________________________________________________________________________Date:_____/_____/__________ Fill-in-the-table: 1) Remember the 4 ways to represent a function? They are . . . Equation _____________ Table ______________ Solve the following linear equations (plug x into equation): 2) y = 3x – 2 x y 3) x + y = 8 -1 -1 0 0 1 1 2 2 Multiple Choice: 4) Which equation represents the following function table? x y -1 -7 0 -2 1 3 2 B. y = 5x D. y = 5x - 2 Magic # . . . 5) Which equation represents the following function table? Can you use magic # here?? A. y = x + 5 C. y = x + 6 8 x y -5 -20 0 0 5 20 10 40 x A. y = 20x B. y = x + 20 C. y = 4x D. y = 2x + 10 y 6) Which table represents the following equation? A. y = 3x - 1 Plug ALL x values into equation BEFORE you choose table . . . 7) Which table represents the following equation? C. A. y = -4x + 1 Plug ALL x values into equation BEFORE you choose table . . . C. x y x y -1 -4 -1 -4 0 --1 0 --1 1 2 1 2 2 6 2 5 x y x y -1 2 -1 -4 0 -1 0 -1 1 2 1 2 2 5 2 7 x y 0 1 1 B. D. x y 0 1 -3 1 -3 2 -7 2 -9 3 -12 3 -13 x y x y -2 9 -5 21 0 1 -2 9 2 -7 1 -3 4 -15 4 -17 B. D. Today’s Lesson: What: Graphing linear equations Why: To use “slope-intercept form” in order to graph linear equations. y = mx + b Remember . . . A linear equation is an equation with 2 different variables (like y = 4x + 1 )– with no exponents. Also, they graph as a ___________________ line! straight Well, when a linear equation is written in a specific order/ format, we call it slope- intercept form . . . In other words, when the equation is written like this: y = 5x + 2 Y is isolated on one side, and the x term comes before the constant! The slope-intercept formula is: y= mx + b What is y = mx + b ?? Well, the m variable stands for ____________, slope & the b variable stands for the y-intercept. steep slope – measure of how ______________ a line is. It is often described as a ratio of a line’s 𝑟𝑖𝑠𝑒 (𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒) rise over its run –( ). 𝑟𝑢𝑛 (ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒) y-intercept– point where the line crosses the ____________________ . y axis Consider the diagram . . . Let’s apply it . . . 1) y = mx + b y = 3x + 2 Step 1: Identify the “m” and the “b” : 𝟑 m = 3 or 𝟏 b=2 Step 2: Plot the y-intercept or b Step 3: Apply slope--rise 3 and run 1 . . . Positive slopes will always graph as UPHILL lines! 2) y = -4x + 6 y = mx + b m = -4 b= 6 Negative slopes will always graph as DOWNHILL lines! When the slope is negative, we FALL instead of RISE . . . 3) y= 𝟏 x 𝟐 m= -3 𝟏 𝟐 b = -3 y = mx + b What if we have the graph Only?? We can easily use “y = mx + b” to come up with the equation as well! How? Study the graph of the line. Identify the y-intercept ____________ (where it crosses the y axis). This is the “b.” Then, determine the slope. Is it an uphill or a downhill? This tells you whether the slope is positive or ___________. negative Count the “rise” grid moves versus the “run” grid moves. This is the “m.” 𝟑 4) m = - 𝟒 b = -2 So, the equation is . . . 𝟑 y = - 𝟒 x + (-2) ________________ Downhill means negative slope! 5) Uphill means positive slope! y = mx + b m= 𝟐 𝟏 b= 2 y = 2x + 2 So, the equation is . . . ________________ 6) Downhill means negative slope! y = mx + b m= - 𝟏 𝟓 b = -3 𝟏 y = - 𝟓 x + (-3) So, the equation is . . .________________ END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day. NAME: Math-7 NOTES DATE: ______/_______/_______ What: Graphing linear equations Why: To use “slope-intercept form” in order to graph linear equations. A linear equation is an equation with 2 different variables (like y = 4x + 1 )– with no exponents. Also, they graph as a ___________________ line! Well, when a linear equation is written in a specific order/ format, we call it slopeintercept form . . . In other words, when the equation is written like this: y = 5x + 2 The slope-intercept formula is: y= mx + b Y is isolated on one side, and the x term comes before the constant! What is y = mx + b ?? Well, the m variable stands for _________________________, & the b variable stands for the y-intercept. slope – measure of how ______________ a line is. It is often described as a ratio of a line’s rise over its 𝑟𝑖𝑠𝑒 (𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒) run –( 𝑟𝑢𝑛 (ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒) ). y-intercept– point where the line crosses the _____________________________________ . Consider the diagram . . . What if we have the graph Only?? We can easily use “y = mx + b” to come up with the equation as well! How? Study the graph of the line. Identify the ____________ (where it crosses the y axis). This is the “b.” Then, determine the slope. Is it an uphill or a downhill? This tells you whether the slope is positive or __________________. Count the “rise” grid moves versus the “run” grid moves. This is the “m.” _________ _________ NAME:________________________________________________________________________________ DATE: _____/_____/__________ Math-7 CLASSWORK “Function representations” Apply everything we have learned in this unit in order to fill in blank spaces: Equation Words Table Graph 1) y = 3x - 2 “y is equal to the product of 3 and a number, minus 2.” x y -1 0 1 2 2) y = x – 4 x y 0 1 2 3 3) “Three more than a number is equal to y.” x y -3 0 3 6 4) “ y equals twice a number, decreased by 3.” x 0 1 2 3 y Equation Words Table Graph 5) x y -1 -4 0 -1 1 2 2 5 Magic # . . . 6) x y -1 -1 0 1 1 3 2 5 Magic # . . . 7) x y 0 1 2 3 y = mx + b 8) x y -1 0 1 2 y = mx + b NAME:________________________________________________________________________________ DATE: _____/_____/__________ Math-7 Homework Graph the following equations (use y = mx + b): 1) y = -4x + 7 3) y= 3 2 x -5 ( m = _____; b = _____ ) ( m = _____; b = _____ ) 2) 4) y= 2 x–4 ( m = _____; b = _____ ) y=- x+8 ( m = _____; b = _____ ) 3 1 2 Study graphs and write the equation (use y = mx + b): 5) ( m = _____; b = _____ ) 6) Equation:____________________________ 7) ( m = _____; b = _____ ) Equation:____________________________ ( m = _____; b = _____ ) Equation:_____________________________ 8) ( m = _____; b = _____ ) Equation:_____________________________