MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

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1 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) -INTERCEPT = the point where the graph touches or crosses the -ais. It occurs when = 0. ) -INTERCEPT = the point where the graph touches or crosses the -ais. It occurs when = 0. CALCULATING & -INTERCEPTS I) An intercept is a point where the graph touches or crosses an ais, either the or the -ais. The -intercept is the point where the graph touches or crosses the -ais. The -intercept is the point where the graph touches or crosses the X-ais. A) THE -INTERCEPT IS THE POINT WHERE THE GRAPH TOUCHES OR CROSSES THE Y-AXIS. 1) INVESTIGATION 1: Use the graphs found at the top of page 9 and question (c) of page 303 of our tet to answer these questions. {Answers are on page 7 of these notes.} a) Determine the coordinates of the -intercept of each graph. Top of pg. 9 pg. 303 Q# (c) b) What do the -intercepts of each graph have in common? c) What do ou think is the same for ever -intercept of ever graph have? ) USE THESE STEPS TO CALCULATE THE -INTERCEPT 1: Substitute each variable with zero (0). : Solve for. 3) SAMPLE PROBLEMS 1: Calculate the -intercept of the graphs of these equations. Be sure ou understand and memorize the process used to complete them. 1) = 3 ) = + 9 3) = ) REQUIRED PRACTICE 1: Calculate the -intercept of the graphs of these equations. SHOW YOUR PROCESS!! {Answers are on page 7 of these notes.} 1) = ) = 5 3) = 5 ) = + 5) = + 3 ) = ) = 3 ( ) + 5 ) = ) = +3+

2 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - B) THE -INTERCEPT IS THE POINT WHERE THE GRAPH TOUCHES OR CROSSES THE X-AXIS. 1) INVESTIGATION : Use the graphs found at the top of page 9 and the middle of page 9 of our tet to answer these questions. {Answers are on page 7 of these notes.} a) Determine the coordinates of the -intercept(s) of each graph. Top of pg. 9 Middle of pg. 9 b) What do the -intercepts of each graph have in common? c) What do ou think is the same for ever -intercept of ever graph have? ) USE THESE STEPS TO CALCULATE THE -INTERCEPT 1: Substitute each variable with zero (0). : Solve for. 3) SAMPLE PROBLEMS : Calculate the -intercept of the graphs of these equations. Be sure ou understand and memorize the process used to complete them. 1) = 3 ) = + 9 3) = 3 ) REQUIRED PRACTICE : Calculate the -intercept of the graphs of these equations. SHOW YOUR PROCESS!! {Answers are on page 7 of these notes.} 1) = ) = 5 3) = 5 GRAPHING LINEAR EQUATIONS USING & -INTERCEPTS I) Recall that all linear equations have these three characteristics: All linear equations: 1. have two different variables that lack visible eponents.. have variables that are not inside a radical sign ( ), absolute value bars ( ), or a denominator. 3. produce straight-line graphs that lean left (!) or right (!). II) Linear equations can be graphed on a grid using onl the & -intercepts. A) USE THESE STEPS TO GRAPH A LINEAR EQUATION USING THE & -INTERCEPTS 1: Calculate the -intercept. : Calculate the -intercept. 3: Set up a grid (REMEMBER TO LABLE AND SHOW THE SCALE OF EACH AXIS). : Plot the & -intercepts. 5: Use a ruler to connect the & -intercepts (REMEMBER TO LABLE THE LINE WITH THE EQUATION).

3 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 3 B) SAMPLE PROBLEMS 3: Graph these linear equations using the & -intercepts. Be sure ou understand and memorize the process used to graph them. 1) = 7 ) + 5 = 1: Calculate the -intercept. (REMEMBER IT OCCURS WHEN = 0) : Calculate the -intercept. (REMEMBER IT OCCURS WHEN = 0) 3: Set up a grid (REMEMBER TO LABLE AND SHOW THE SCALE OF EACH AXIS). : Plot the & -intercepts. 5: Use a ruler to connect the & -intercepts (REMEMBER TO LABLE THE LINE WITH THE EQUATION) C) REQUIRED PRACTICE 3: Instructions: Graph these linear equations using the & -intercepts. (You can use the grids provided on pages 7,, 9 & of these notes. {Ans. See our teacher.} 1) = +5 ) = + 3) 3 + =1 ) 3 5 =1 5) = 3 + ) = 3 5 7) 3( )=1 ) =

4 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) SLOPE -INTERCEPT FORM = a linear equation is in slope -intercept form when it is written in this pattern: = m +b where m 0. Slope -intercept form is also called general form. ) SLOPE = m = a number describing the steepness of a graphed line. Slope is alwas written as a fraction. 3) -INTERCEPT = b = the point where the graphed line touches or crosses the -ais. SLOPE -INTERCEPT FORM I) WRITING A LINEAR EQUATION IN SLOPE -INTERCEPT FORM A) A LINEAR EQUATION IS IN SLOPE Y-INTERCEPT FORM WHEN IT IS WRITTEN IN THIS PATTERN: = m + b where m is the slope and b is the -intercept. The slope, m, is a measure of how much the linear equation s graph leans. The -intercept is the point where the linear equation s graph touches or crosses the -ais of the grid. Stud these eamples carefull. Be sure ou understand wh the linear equations in the left hand column are in slope -intercept form while the linear equations in the right hand column are not in slope - intercept form. SLOPE -INTERCEPT FORM NOT SLOPE -INTERCEPT FORM = +1 = 1 = 0.5 = = = = = 3 1)The linear equations in the left hand column are in slope -intercept form because the -term is isolated (b itself) and on the left side of the equal sign. ) The linear equations in the right hand column are in NOT in slope -intercept form. a) = 1 is not in slope -intercept form because the -term is not isolated (b itself). b) 5 = + 15 is not in slope -intercept form because the -term has a coefficient, it is not isolated. c) = is not in slope -intercept form because the -term is not isolated. d) = 3 is not in slope -intercept form because the constant term is written before the -term. B) The process used to write a linear equation in slope -intercept form is the same process used to isolate a variable described on page of Topic. 1) SAMPLE PROBLEMS 7: Stud these eamples carefull. Be sure ou understand and memorize the process used to complete them. INSTRUCTIONS: Write these linear equations in slope -intercept form. a) 3 + = b) = ) REQUIRED PRACTICE : Write these equations in slope -intercept form. SHOW YOUR PROCESS!! {Answers are on page 7 of these notes.} 1) = 3 ) 5 3 = 3) = 0

5 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 5 II) WHEN THE EQUATION OF A LINEAR EQUATION IS WRITTEN IN SLOPE -INTERCEPT FORM: = m +b, two etremel valuable pieces of information are instantl revealed: The FIRST is b, which is the -intercept; The SECOND is m, which is the slope. You must be able to state the -intercept and the slope of an linear equation. A) SAMPLE PROBLEMS 5: Stud these eamples carefull. Be sure ou understand and memorize the process used to complete them. INSTRUCTIONS: Write the -intercept and the slope of these linear equations. LINEAR EQUATION b m 1) = 3 ) = ) = B) REQUIRED PRACTICE 5: Write the -intercept and the slope of these linear equations. {Answers are on page 7 of these notes.} 1) = 3 ) = 3 + 3) = 9 7 EXPLAINING SLOPE -INTERCEPT FORM I) THE -intercept AND THE SLOPE ARE ALL THAT YOU NEED TO DRAW THE GRAPH OF ANY LINEAR EQUATION A) The -intercept, b, is the point where the graph touches or crosses the -ais. Stud this graph. 1) The graph to the right has the equation written in slope -intercept form as = This equation has a -intercept of b = 1 which means its graph touches or crosses the -ais at = 1. B) The SLOPE, m, is a number describing the steepness of a linear function s graph. Slope is best written as the fraction m = rise up or down on the ais, which means m =. Slope is used to create points on a grid, run left or right on the ais which are connected together to create the linear equation's leaning straight-line graph. 1) i.e. If m = 3, starting at the -intercept, move positive spaces up the -ais, then move positive 3 spaces right on the -ais, then plot a point. Continuing to use this pattern of up, right 3, plotting points until ou run out of space on the grid. ) i.e. If m = 5, starting at the -intercept, move negative spaces down the -ais, then move positive 5 spaces right on the -ais, then plot a point. Continuing to use this pattern of down, right 5, plot a point until ou run out of grid. You can also view this slope as m = 5, which means starting at the -intercept, more positive spaces up on the -ais, then move negative 5 spaces left on the -ais, then plot a point. Continue using this pattern of up, left 5, plotting points until ou run out of space on the grid.

6 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - GRAPHING LINEAR EQUATIONS USING SLOPE -INTERCEPT FORM I) IN ORDER TO GRAPH LINEAR EQUATIONS, THEIR EQUATIONS MUST BE WRITTEN IN SLOPE -INTERCEPT FORM, WHICH IS = m +b, where m 0. When a linear equation is written in slope -intercept form, its graph can be drawn on a grid b one of these three methods. 1. Create a table of ordered pairs b choosing values of, to substituting them into the equation, calculating values of, then plotting the ordered pairs on a grid.. Input the equation into the graphing calculator, obtain the ordered pairs from the TABLE window of the graphing calculator, then plot the ordered pairs on a grid. 3. Use the -intercept and the slope from the equation to draw the graph directl from the equation. II) USE THESE STEPS TO GRAPH A LINEAR EQUATION STEP 1: Write the linear function in slope -intercept form. STEP : Set up a grid and plot the -intercept. STEP 3: Use the slope to create as man other points as can fit on the grid. STEP : Use a RULER to connect the points; then label the graph with the equation. A) SAMPLE PROBLEMS : Stud these eamples carefull. Be sure ou understand and memorize the process used to complete them. 1) Graph = 3 STEP 1: Write the linear equation in slope - intercept form. STEP : Set up a grid and plot the -intercept. -intercept = STEP 3: Use the slope to create as man other points as can fit on the grid. slope = STEP : Connect points with a RULER then label the graph with the equation ) Graph 3 + = 9 STEP 1: Write the linear equation in slope - intercept form. STEP : Set up a grid and plot the -intercept. -intercept = STEP 3: Use the slope to create as man other points as can fit on the grid. slope = STEP : Connect points with a RULER then label the graph with the equation

7 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 7 B) REQUIRED PRACTICE : Graph these linear equations on a grid. You can use the grids on pages 7,, 9 &. SHOW THE PROCESS!! {Ans. See our teacher} 1) = 3 3 ) = ) = ) + 7 = 1 5) = 1 ) 3 1 = 0 INVESTIGATION 1 from page 1 1) ( 0, ); 0, 3 ( ) ) = 0 3) = 0 ANSWERS TO THE REQUIRED PRACTICE Required Practice 1 from page 1 1) = ) = 3) = ) = 0 5) = 3 ) = 7) = 13 ) = 1 3 9) = 0 INVESTIGATION from page 1a) ( 5, 0);, 0 ( ) 1b) = 0 1c) = 0 Required Practice from page 1) = ) = 3) = 15 Required Practice from page 1) = 3 ) = ) = 3 + Required Practice 5 from page 5 1) b = 3, m = 1 ) b =, m = 3 3) b = 7, m =

8 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW DO NOT USE FOR ASSIGNMENTS

9 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW DO NOT USE FOR ASSIGNMENTS

10 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW DO NOT USE FOR ASSIGNMENTS

11 FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 11 LAST then FIRST Name T9 GRAPHING LINEAR EQUATIONS REVIEW - Block: Show the process required to complete each problem to avoid receiving a zero grade. Neatness Counts!!! (Marks indicated in italicized brackets.) REMEMBER TO USE GRID PAPER FOR ALL ASSIGNMENTS!!! Cop the sentences numbered 1 - then match it with the correct term listed below. (0.5 marks each) Ordered pair Origin Range Domain Variable -intercept -intercept Constant term Coefficient -ais -ais Equation 1) The values of the vertical ais used to draw the graph. ) Point where the graph touches or crosses the -ais. 3) The group of numbers composed of all the first numbers of a set of ordered pairs. ) Point where the graph touches or crosses the -ais. Graph these equations using the -intercept and the -intercept. State the domain and range of the graph. 5) = 7 (7.5) ) + 5 = 15 () REMEMBER TO STATE THE -INTERCEPT AND SLOPE WHEN GRAPHING USING SLOPE -INTERCEPT FORM!!! Graph these equations using slope -intercept form. State the domain and range of the graph. 7) = (5) ) 3 = 1 (.5) Following the instructions. (1) /3