Factor Vocab Word 2 Sometimes when you subtract the fractions, - PDF document

Slide 1 / 309 Slide 2 / 309 Graphing Linear Equations 8th Grade 2015-01-26 www.njctl.org Slide 3 / 309 Slide 4 / 309 Table of Contents click on the topic to go · Vocabulary Review Links to PARCC sample questions to that section · Tables · Slope & y-intercept · Defining Slope on the Coordinate Plane · Tables and Slope Non-Calculator #3 Calculator #4 · Slope Formula Non-Calculator #7 Calculator #6 · Slope Intercept Form · Rate of Change Non-Calculator #11 Calculator #7 · Proportional Relationships and Graphing Non-Calculator #16 Calculator #8 · Slope and Similar Triangles · Parallel and Perpendicular Lines Calculator #9 · Solve Systems by Graphing · Solve Systems by Substitution Calculator #12 · Solve Systems by Elimination · Choosing Your Strategy · Writing Systems to Model Situations · Glossary Slide 5 / 309 Slide 6 / 309 The charts have 4 parts. Vocabulary words are identified with a 1 dotted underline. Factor Vocab Word 2 Sometimes when you subtract the fractions, Its meaning you find that you can't because the first (As it is used numerator is smaller than the second! When A whole number A whole number that can divide into that multiplies with in the this happens, you need to regroup from the another number another number to whole number. (Click on the dotted lesson.) with no remainder. make a third number. underline.) How many thirds are in 1 whole? 5 .1 R 15 3 5 3 16 How many fifths are in 1 whole? 3 is a factor of 15 3 is not a 3 x 5 = 15 factor of 16 How many ninths are in 1 whole? 3 Back to 3 and 5 are 4 Instruction factors of 15 Examples/ The underline is linked to the glossary at the end of the Link to return to the Notebook. It can also be printed for a word wall. Counterexamples instructional page.

Slide 7 / 309 Slide 8 / 309 Vocabulary Review To graph an ordered pair, such as ( 4, 8), you start at the Coordinate Plane: the two dimensional plane or flat surface that origin (0, 0)and then go left or right on the x-axis is created when the x-axis intersects with the y-axis. Also known as a coordinate graph and the Cartesian plane. depending on the first number and then up or down from there parallel to the y-axis. Quadrant: any of the four regions created when the x-axis intersects the y-axis. They are usually numbered with Roman I II numerals. 10 8 6 x-axis: horizontal number line 4 that extends indefinitely in 2 IV III both directions from zero. 0 -10 -8 -6 -4 -2 2 4 6 8 10 -2 (Right- positive Left- negative) -4 -6 -8 y-axis: vertical number line that extends indefinitely in both -10 directions from zero. (Up- positive Down- negative) Origin: the point where zero on the x-axis intersects zero on the y-axis. The coordinates of the origin are (0,0). Slide 9 / 309 Slide 10 / 309 So to graph (4,8), we would go 4 to the right and up 8 from there. 10 (4,8) 8 Linear Equation: 6 4 2 Any equation whose graph is represented by a straight line. 0 -8 -4 -2 -10 -6 2 4 6 8 10 -2 -4 One way to check this is to create a -6 -8 table of values. -10 Slide 11 / 309 Slide 12 / 309 Geometry Theorem: Tables Through any two points in a plane there can be drawn only one line. Return to Table of Contents

Slide 13 / 309 Slide 14 / 309 One way is to create a table of values. Given y=3x+2, we want to graph our equation to show all of the Let's consider the equation y= 3x + 2. ordered pairs that make it true. 10 We need to find pairs of x and y 8 So according to this theorem from 10 numbers that make equation true. 6 8 Geometry, we need to find 2 4 6 points. 2 4 2 0 -10 -8 -6 -4 -2 2 4 6 8 10 -2 0 -8 -4 -2 -10 -6 2 4 6 8 10 -4 -2 -6 -4 -8 -6 -10 -8 -10 Slide 15 / 309 Slide 16 / 309 Now let's graph those points we Let's find some values for y=3x+2. just found. 10 Pick values for x and plug them 8 into the equation,then solve for y. 6 x 3(x)+2 y (x,y) 4 -3 3(-3)+2 -7 (-3,-7) 2 10 x 3(x)+2 y (x,y) 0 3(0)+2 2 (0,2) 8 0 -10 -8 -6 -4 -2 2 4 6 8 10 -3 3(-3)+2 -7 (-3,-7) -2 6 2 3(2)+2 8 (2,8) 0 3(0)+2 2 (0,2) -4 4 -6 2 2 3(2)+2 8 (2,8) Notice anything about the points -8 0 -10 -8 -6 -4 -2 2 4 6 8 10 -10 -2 we just graphed? -4 -6 -8 -10 Slide 17 / 309 Slide 18 / 309 That's right! The points we graphed form a line. Graph y = 2x+4 The theorem says we only needed 2 points, so why did we graph 3 points? click for table x 2x+4 y (x,y) x 2x+4 y (x,y) The third point serves as a check. 10 0 2(0)+4 4 (0,4) 8 y 3 2(3)+4 10 (3,10) 6 10 -1 2(-1)+4 2 (-1,2) 4 8 2 6 10 4 0 Now graph your points -8 -4 -2 -10 -6 2 4 6 8 10 8 -2 2 and draw the line. 6 -4 x 0 -8 -4 -2 -10 -6 4 2 4 6 8 10 -6 -2 2 -8 -4 -10 -6 0 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -8 -4 -10 -6 -8 -10 Click for graph

Slide 19 / 309 Slide 20 / 309 Graph y = -2x+1 Graph y = ¾x-3 click for table click for table x -2(x)+1 y (x,y) x -2(x)+1 y (x,y) x ¾(x)-3 y (x,y) x ¾(x)-3 y (x,y) 0 -2(0)+1 1 (0,1) 0 ¾ (0)-3 -3 (0,-3) 3 -2(3)+1 -5 (3,-5) y -1 -2(-1)+1 3 (-1,3) 4 ¾ (4)-3 0 (4,0) 10 y 10 8 -4 ¾ (-4)-3 -6 (-4,-6) 8 6 10 10 6 4 8 Now graph your points 8 2 4 6 and draw the line. 6 2 Now graph your points 4 x 0 -8 -6 -4 -2 -10 2 4 6 8 10 4 -2 2 x and draw the line. 0 -8 -4 -2 -10 -6 2 4 6 8 10 2 -2 -4 0 -10 -8 -6 -4 -2 2 4 6 8 10 -4 -6 -2 0 -2 -10 -8 -6 -4 2 4 6 8 10 -2 -6 -8 -4 -4 -8 -10 -6 -10 -6 -8 -8 -10 -10 Click for graph Click for graph Slide 21 / 309 Slide 21 (Answer) / 309 Recall that in the previous example Recall that in the previous example that even though the number in front that even though the number in front of x was a fraction, our answers were of x was a fraction, our answers were x ¾(x)-3 y (x,y) x ¾(x)-3 y (x,y) integers. integers. 0 ¾ (0)-3 -3 (0,-3) 0 ¾ (0)-3 -3 (0,-3) 4 ¾ (4)-3 0 (4,0) 4 ¾ (4)-3 0 (4,0) Why? Discuss at your table. Why? Discuss at your table. The x-values chosen are -4 ¾ (-4)-3 -6 (-4,-6) -4 ¾ (-4)-3 -6 (-4,-6) Answer zero, the denominator and the opposite of the denominator. [This object is a pull tab] Slide 22 / 309 Slide 23 / 309

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Slide 30 / 309 Slide 31 / 309 Slide 32 / 309 Slide 32 (Answer) / 309 11 A solution is 20% bleach. 11 A solution is 20% bleach. Create a graph that represents all possible Create a graph that represents all possible combinations of the number of liters of bleach, combinations of the number of liters of bleach, contained in the number of liters of the solution. contained in the number of liters of the solution. To graph a line, pick two points on the coordinate To graph a line, pick two points on the coordinate Students type their answers here Students type their answers here plane. A line will be drawn through the points. plane. A line will be drawn through the points. Answer [This object is a pull tab] From PARCC sample test From PARCC sample test Slide 33 / 309 Slide 34 / 309 The Equation of a Line You only need a few 10 facts about a line to 8 completely describe it: 6 Slope & y-intercept · Its y-intercept (where it 4 crosses the y-axis) on the Coordinate Plane 2 "b" 0 -8 · Its slope (how much it -10 -6 -4 -2 2 4 6 10 8 -2 rises or falls) Return to Table -4 "m" of Contents -6 · y = mx + b -8 -10

Slide 35 / 309 Slide 36 / 309 Consider this graph of the Cartesian The y-intercept Plane, also called a Coordinate Plane or XY-Plane. The y-intercept ("b")of a line 10 is the point where the line 8 intercepts the y-axis. 6 In this case, the y-intercept 4 of the line is +4. 2 0 -8 -10 -6 -4 -2 2 4 6 8 10 -2 Imagine trying to tell a person how This is the ordered pair (0,4). -4 to draw a line on the Cartesian -6 Plane. -8 -10 Slide 37 / 309 Slide 37 (Answer) / 309 12 What is the y-intercept of this line? 12 What is the y-intercept of this line? 10 10 8 8 6 6 Answer b = 6 4 4 2 2 0 0 -10 -8 -6 -4 -2 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 6 8 10 -2 -2 [This object is a pull tab] -4 -4 -6 -6 -8 -8 -10 -10 Slide 38 / 309 Slide 38 (Answer) / 309 13 What is the y-intercept of this line? 13 What is the y-intercept of this line? 10 10 8 8 6 6 Answer 4 4 b = -4 2 2 0 0 -8 -8 -10 -6 -4 -2 2 4 6 8 10 -10 -6 -4 -2 2 4 6 8 10 -2 -2 -4 -4 [This object is a pull tab] -6 -6 -8 -8 -10 -10