Ke Focus #6 - Finding the Slope of a Line Between Two Points. Given the following equations of lines, find the SLOPES of the lines: = + 6... + 8 = 7 9 - = 7 - - 9 = 4.. 6. = 9-8 - = + 7 = 4-9 7. 8. 9.. Given the following pairs of points, find the slope AND equation of the line.. (, 4 ) and ( -, ). ( - 7, - ) and ( -, - ). (, 6 ) and ( -, - ) Answeke. m =. m = -. m = 4. m = -. m = 9 6. m = - 7. m = 8. m = - 9 8 9 9 9. m = 4. m = - + 4-7 =. m = 4 4 - + =. m = 7 7-6 + = 4 6
Ke Focus #6 - Finding the Slope and EQUATION OF A LINE Find the Slope of the Following Lines: + = + 8 = - - 7 = 9... 7-4 = - - 4 + = - 6 - = 9 4.. 6. If each of the following lines are Direct Variations, provide the Equation of each line in standard form, given the m : 7. m = 8. m = - 4 9. m =. 7 m = Find the equation of the line through the given point having the given slope:. m =, ( -, 4 ). m = - 4, (, 6 ) 7. m = -, ( -, - ) 4. m =, (, - ) Answerke - - 7.. 4 8 7 4. 6. - 7. - = 8. 4 + 7 = 9. - =. - =. - + 6 =. 4 + 7-6 =. + + = 4. - - 4 =
Ke Focus # 6 - Points of Intersection Graphing line equations that appl to a real world problem. For each of the five scenarios, write the line equations, graph both lines and state the P.O.I. Scenario : The Acme Yearbook Compan charges $ to set up the laout of the book and $ for each earbook. Equation : The Qualit Yearbook Compan charges $ to set up the laout of the book and $ for each earbook. Equation : POI : When would ou use Acme Yearbook Compan and when would ou use Qualit Yearbook Compan? Scenario : The school basketball team is traveling b bus to a competition. The Orange Bus Compan charges a flat rate of $ plus an additional charge of $4 for each athlete that travels on the bus. Equation : The Yellow Bus Compan charges a flat rate of $, plus an additional charge of $8. Equation : POI : Scenario : Acme: = + Qualit: = + POI (4,7) Qualit - 4 books Acme >4 Scenario : Orange: = 4 + Yellow: = 8 + POI (, ) Yellow - Orange >
Ke Focus # 6 Solving Sstems of Equations Scenario : The three window cleaning companies offer the following prices: Price A: $ for supplies, plus $4 per window Price B: $7 per window. You have windows to clean. Equation for Price A : Equation for Price B : Which would ou choose and wh? Scenario 4: Three book binding companies offer the following prices: Price A: $ for shipping, plus $4. per book Price B: $ for shipping, plus $. per book Price C: $8 per book. You want to have a maimum of books bound. Equation for Price A : Equation for Price B : Equation for Price C : Scenario : The price for Decorator A is $ for the first visit, plus $/h The price for Decorator B is $ for the first visit, plus $/h The price for decorator C is $ for the first visit, plus $/h Equation for Price A : Equation for Price B : Equation for Price C : Scenario : A: = 4 + B: = 7 POI(, 7) Use price A for windows Scenario 4: A: = 4. + B: = + C: = 8 For books, use C Scenario : A: = + B: = + C: = + -, use A, - use C, > use B
Ke Focus # 7. A square has vertices A(, 4 ), B ( - 6, ), C ( -, - 6 ) and D( 4, - ). Draw the SQUARE on a grid. a) Determine the equations of the lines containing the four sides. b) Determine the equations of the lines containing the two diagonals. Answerke AB: BC: CD: AD: AC: = + 4 BD:
Ke Focus # 7 - Where do the Meet? Where do the Meet? The Nguen famil lives in Thunder Ba. The Berg famil lives in Kenora. At noon, the Nguens leave b car on a trip to Kenora and drive at an average speed of 7km/h. At the same time, the Bergs leaves b car on a trip to Thunder Ba. The drive at an average speed of 8km/h. It is approimatel m from Kenora to Thunder Ba. Where are the two cars when the meet? a)complete the table to show how far the Nguen famil is from Thunder Ba after each hour of the trip. Time ( h ) 4 6 7 8 Distance from Thunder Ba (km) b) Draw a graph of distance from Thunder Ba against time for the Nguen famil a) Cop and complete the table to show how far the Berg famil is from Thunder Ba after each hour of the trip: Time ( h ) 4 6 7 8 Distance from Thunder Ba (km) b) Use the same grid as in eercise b. Draw a graph of distance from Thunder Ba against time for the Berg famil.. The two lines ou drew in eercise and should intersect. What are the coordinates of the point where the lines intersect? What do these coordinates tell ou about the locations of the two cars? The meet at.4hours into the trip, 8km from Thunder Ba
Ke Focus # 7 - Equations of Lines Complete the Chart Equation Slope -intercept Slope of Line parallel to this line. = + Slope of Line Perpendicular to this Line. = - - 7. = + 4.. 6. 7. 7 8-4 - 4 8. 9. =. = 7. =. a) On a grid, draw a line with slope through A ( -, ) b) Draw a line through C ( -, - ) that is parallel to the line in part a. c) Draw a line through C ( -, - ) that is perpendicular to the line in part a.. a) On the same aes, draw a line through P(, ) with each of the following slopes: i) ii) - iii) - iv) v) Not defined b a real number. 4 7 b) Choose one slope from part a. Write to eplain how ou drew the line. 4. Which of these points lie on the line = + 4 a) C (, ) b) D ( 7, 4 ) c) E ( -, ) d) F( 8, 4 ) e) G (., ). Determine the equation of the line that passes through each pair of points. a) A (, ) and B ( -, - ) b) C (- 4, 7 ) and D (, - 4 )
6. Determine the equation of the line that passes through J (, ) and is : a) Parallel to the line = - - 4 b) Perpendicular to the line = - + 4 7. Graph each line without making a table of values. a) - + = b) + = c) + - = 8. Solve each linear sstem. a) + = - 8 b) + = 6 - = 7 - =
Ke Focus # 7 - Answers. Complete the Chart. Graph Equation Slope b parallel Perpendicular. = +. = - - 7 - - 7 - -. = + - 4. = + 7. = - 4 + 8 6. = -4 + 7-4 8-4 - 4-4 - 4 4 7. = + - 8. = - 9. =. = 7-7 undefined. = undef doesn t cross undefined v) =. 4. a) Yes b) No c) No d) Yes e) Yes iv) = ii) = - + 4 4. a) = + b) = - + 9 9 9 6. a) = - + b) = + 4 4 i) = - 4 7. Graph iii) = - + 9 7 7 8. a) ( -, - ) b) ( 4, ) a) = + 4 c) = - + b) = -
Grade 9 Assessment of Mathematics Student Answer Sheet Your multiple-choice answers must be entered on this sheet ACADEMIC To indicate our answer, use a pencil to fill in the circle completel Like this: Not Like This: Do not fill in more than one answer to a question Do not leave a question blank. Cleanl erase an answer ou wish to change and fill in the circle for our new answer. a b c d 6. a b c d. a b c d 6. a b c d, a b c d 7. a b c d. a b c d 7. a b c d. a b c d 8. a b c d. a b c d 8. a b c d 4. a b c d 9. a b c d 4. a b c d 9. a b c d. a b c d. a b c d. a b c d. a b c d. Which of the following points is in the third quadrant of the -plane?. Which graph is the best match to a sketch of = 4? a) (, 7 ) b) (, - 7 ) c) ( -, 7 ) d) ( -, - 7 ). The points ( -, - 4 ) and ( 6, ) are marked on an -plane. A B C D C Which statement about the line through (, 4) and (6, ) is not true? a) Its -intercept is. b) Its slope is positive. c) Its -intercept is. d) It passes through (4, 9).
4. PQ and RS are parallel line segments. What is the value of? 6. A is the point ( -, ), B is the point (, - 4) and D is the point (, 6). a) b) 6 c) 7 d) 8. If A is (, 4) and B is (7, ), which point is on the line segment AB? If ABCD is a rhombus, which of the following is point C? a) (, ) b) (, 4 ) c) ( 4, ) d) ( 4, 4 ) 7. Which of the following tables of values represents the linear relationship =? a) 4 c) 6 a) (, ) b) ( 4, 8 ) c) (, 9 ) d) ( 6, ) b) 8 4 6 d) 4 6 6 8. Which of the following properties does the line have? a) positive slope and positive -intercept b) positive slope and negative -intercept c) negative slope and positive -intercept d) negative slope and negative -intercept
9. Which points on the graph have the same -coordinates?. Four points, A, B, C and D, are marked on an -plane and joined b line segments as shown. a) A and B b) A and C c) B and C d) B and D Which line segment has a negative slope? a) BA b) BC c) CD d) AD. The graph shows a scatter plot and a line of best fit.. Which of the following equations is equivalent to - = 4? a) = - 9 b) = - + 9 c) = - 4 d) = - + 4 Which of the following statements about the line of best fit is true? a) The line has a negative slope and a negative -intercept. b) The line has a negative slope and a positive -intercept. c) The line has a positive slope and a negative -intercept. d) The line has a positive slope and a positive -intercept.. Which of the following lines has the same slope as the line - + = a) = - + b) = - + c) = - - d) = -
4. Which graph below is likel the graph for =? a) b) * G 7. Natasha works for a computer compan. The table shows her annual salar in the last five ears. Year Annual Salar ($) 6 c) d) 4 6 8 8 4 If the trend continues, what will Natasha s annual salar be in the 8th ear?. The total cost, C, in dollars, of running an advertisement in a newspaper is made up of an initial cost of $, plus a charge of $ per da, where n represents the number of das. Which equation represents this relationship? a) C = n + b) C = + n c) C = ( + )n d) C = + n 6. Ivan sells programs at a baseball game. He earns $ per game plus $ for each bo of programs he sells. If represents the number of boes of programs he sells at the game, which of the following epressions represents Ivan s earnings, in dollars, at that game? a) + b) + c) ( + ) d) ( + ) a) $4 b) $4 c) $46 4 d) $49 6 8. Josie works in a sports store. She receives 8% of the total sales each da. One da, she receives $ for her portion of the total sales. What are the total sales for that da? a) $7.8 b) $4.7 c) $8. d) $47. 9. How would the graph of the relation = - change if the and - were both doubled? The graph would be: a) steeper and have a lower - intercept. b) steeper and have a higher -intercept. c) less steep and have a lower -intercept. d) less steep and have a higher -intercept.
.Two biccle repair stores charge an initial fee and an hourl rate for repairs. The graph below shows the total cost of repairs versus time for the repair. Which statement is true? A The two stores charge different hourl rates and the same initial fee. B The two stores charge the same hourl rate and different initial fees. C The two stores charge different hourl rates and different initial fees. D The two stores charge the same hourl rate and the same initial fee. Answers:.D.C.B 4.D.D 6.C 7.C 8.B 9.D.D.D.A.D 4.A.B 6.A 7.B 8.D 9.A.B