MFM2P Linear Relations Checklist 1 Goals for this unit: I can explain the properties of slope and calculate its value as a rate of change. I can determine y-intercepts and slopes of given relations. I can determine the equation of a relation and graph it with the given information. U2L1 Patterns and Ordered Pairs Learning Goal: I can graph relationships using a set of ordered pairs on the Cartesian Plane. U2L2 Slope as a Rate of Change Learning Goal: I know what is meant by slope of a line and how it relates to the rate of change of a relationship. U2L3 Slope and Y-intercept Learning Goal: I know what the slope and y intercept of a line are and how this information is related to the line's equation. U2L4 Properties of Slopes Learning Goal: I can compare the slopes of lines, and can tell which lines are steeper and which lines have a positive or negative slope. U2L5 Equations of Lines Learning Goal: I can determine the equation of a line if I am given a slope and a point, or two points on the line U2L6 Graphing Linear Relations Learning Goal: I can graph linear relationships by hand using a table or from the equation. Note Assigned Work: Worksheet Journal 1 Note Assigned Work: Page 106 # 1-5, 6b, 7, 9, 15 Journal 2 Note Assigned Work: Page 115, # 1-4, 6-9 Journal 3 Note Assigned Work: Page 124, # 1-10, 14, 15 Journal 4 Note Assigned Work: Page 133, # 1-4, 5(every other), 6, 7(every other), 8, 11, 12 Journal 5 Note Assigned Work: Page 143, #1, 3, 5, 7-10, 12 Review Journal 6 Assigned Work: Page 146, All questions
U2L1 Patterns and Ordered Pairs Topic : Relations and Ordered Pairs Goal : I can graph relationships using a set of ordered pairs on the Cartesian Plane. Patterns & Ordered Pairs Quad 2 Quad 1 The Cartesian Plane is a grid, cut into 4 sections by a pair of axis. The VERTICAL axis is the y axis (the dependent axis). The values there depend on the horizontal axis. x axis The HORIZONTAL axis is the x axis (the independent axis). To state a point on the grid, you give its coordinates, x first, then y. The resulting pair of coordinates is called an ORDERED PAIR. (x, y) Quad 3 Quad 4 Example 1. Label the points on the grid above. The centre of the grid, where the axis cross, is called the origin. The coordinates of the origin are (0, 0) Example 2. If plotted points form a straight line (you can put a ruler on them and draw a line through them all) we say that it is a linear relationship. Plot these points do they form a linear relationship. (1, 4) (2, 3) (3, 2) Example 3. A set of points can also be represented in a table of values. Make a table out of the above points.
U2L1 Patterns and Ordered Pairs Example 4. Driving lessons cost $40/h. Make a table of values for up to 6 hours of instruction. Is this direct or partial variation? About how many hours could you you get for $150. x y Pull Example 5. A driver's ed class costs $100 for the class, and $40 for each hour of driving instruction. Make a table of values for up to 6 hours of instruction. Is this direct or partial variation? x y Pull Practice : Handout
U2L2 Slope as a Rate of Change Today's Topic :slope Today's Goal : I know what is meant by slope of a line and how it relates to the rate of change of a relationship. Slope as a Rate of Change Slope... 1. is the steepness of a line 2. compares how far up a line goes (its vertical distance) to how far over it goes (its horizontal distance). rise 3. can be calculated by m= run 4. can be negative if the line goes DOWN as you look from left to right. 5. is larger for lines that are steeper. 6. is the rate of change in a relationship. Finding Slope on a Graph Step 1 locate two points ON a line. Step 2 draw (or imagine) a right triangle between these two points with the line as the hypotenuse. Step 3 determine the lengths of the vertical (rise) and horizontal (run) arms of the triangle. Step 4 calculate m= rise run
U2L2 Slope as a Rate of Change Example 1. Find the slope of the following lines. Note if the line slopes DOWN the rise is negative. Finding Slope From a Table Create a table of values for the relation y = 3x+5 and graph it. Use the table and graph to determine the slope. x y Step 1 determine the change in the y's Step 2 determine the change in the x's Step 3 calculate m= change in y change in x
U2L2 Slope as a Rate of Change Finding Slope from a Relationship Bell Canada has a monthly cell phone plan that costs $10 plus $0.05/text message. The independent variable is The dependent variable is Make a table up to 100 text messages and find the rate of change. Notice anything? Homework Page 106 #1 5, 6b, 7, 9, 15
U2L3 Slope and Y intercept Today's Topic : Today's Goal : slope & y intercept I know what the slope and y intercept of a line are and how this information is related to the line's equation. Slope and y intercept of a line First, let's make a table of values and 2 graph the line y = x + 5 3 x y (x, y) NOTE If the coefficient of x is a fraction, the math is easier if you pick values of x that are multiples of the denominator What is the slope of the line? Where does it cross the y axis? Where have you seen these numbers before? The slope of a line is given the symbol 'm' and the y intercept is given the symbol 'b'. So in general, any line has an equation that is y = mx + b
U2L3 Slope and Y intercept Example 1. What are the slope and y intercept of the following lines a) y = 5x 10 m = b = b) y = 11 0.25x m = b = c) y = 7x 11 m = b = Example 2. Write an equation for a line that has a slope of 6 and a y intercept of 4. Example 3. Write the equation of the given line.
U2L3 Slope and Y intercept Example 4. A plumber charges for his service according to the equation C = 50 + 30t, where C is the total cost of the bill and t is the time in hours it takes to complete the job. a) If we graphed this relation, what would be the y intercept be and what does it represent. b) What is the slope of this equation, and what does it represent? Homework Page 115 #1 4, 6 9
Topic : Goal : Slopes of Lines I can compare the slopes of lines, and can tell which lines are steeper and which lines have a postive or negative slope. Properties of Slopes of Lines Which of the two given lines are steeper? Find their slopes, what do you notice? slope = rise run slope = rise run The steeper the line the larger the number will be for the slope. What is the main difference between the two lines? Find their slopes, what do you notice? slope = rise run slope = rise run As you look from left to right, if a line goes UP the slope is positive, DOWN and the slope is negative.
What kinds of lines are these? Find the slopes - what do you notice? slope = rise run slope = rise run Parallel lines have slopes that are equal. Example 1. For the following lines, state whether the slopes are positive or negative or zero. y=4x+3 y=5-0.6x y=11 Example 2. Compared to y = 3x - 6, write the equation of a line that is... a) steeper b) less steep c) of equal steepness (parallel) d) the same steepness but going in the opposite direction.
Example 3. Each of the following table of values represent a line, determine if the lines in the tables are parallel or not. slope = change in y's change in x's slope = change in y's change in x's Practice Questions Page 124 #1-10, 14, 15
MFM 2P U2L5 Equations of Lines Topic : Equations of Lines Goal : I can determine the equation of a line if I am given a slope and a point, or two points on the line Equations of Lines What is the equation of each line. a) b) A line with slope 3 and y int 5 Just remember y = mx + b! But what if the point we have isn't a y intercept? Finding the equation of a line given slope, and any point y = mx + b is like any other formula. If I know the values of any of the variables I can sub them in and rearrange. Example 1. What is the equation of a line with slope 3, that goes through ( 2, 5)?
MFM 2P U2L5 Equations of Lines Finding the equation of a line from a table of values Remember that when a line crosses the y axis (the y intercept) the x coordinate at that point is 0 x 2 0 2 4 6 y 3 2 7 12 17 So what is the slope and y intercept of this table? The equation of this line is x 3 6 9 12 15 y 2 6 10 14 18 So what is the slope and y intercept of this table? The equation of this line is
MFM 2P U2L5 Equations of Lines Finding the equation of a line from two points What is the equation of the line that passes through ( 2, 3) and (1, 6). Alyssa rented a car for a day. She drove it 240 km and was charged $74. Nathan rented the same car the next day. He drove it 150 km and was charged $65. Find a linear relationship to represent this situation. What does this tell you about how the company charges to rent vehicles? Practice Questions Page 133 #1 4, 5eop, 6, 7eop 8, 11, 12
MFM 2P U2L6 Graphing Linear Relations March 07, 2013 Topic : linear relationships Goal : I can graph linear relationships by hand using a table or from the equation. Graph Linear Relations by Hand If you have the slope of a line and a point on it, you can graph the whole line by remembering rise and run... Example 1. A line with a slope of 5, passes through the point ( 3, 2). Graph the line. Step 1 Step 2 Step 3 Step 4 Plot the point. Take the slope and break it into rise and run. Use the rise and run to move away from the point you plotted. Plot another point. Repeat step 3 for as many times as you like. Then draw a line through your points.
MFM 2P U2L6 Graphing Linear Relations March 07, 2013 Remember when you have an equation, you have the slope and the y intercept. The y intercept is just a point a special point because it is on the y axis, but it's still just a point. So if we have the equation of a line, we have enough information to graph it. 4 Example 2. Graph the line y = x + 2 5 slope = y int. = if the slope is negative put it with the RISE the steps are the same as the last example, you just use the y intercept as the point, then carry on. Example 2. Graph each of the following lines. a) y = 5 2x b) y = 2.5x 3 c) y = 3 x + 3 1 4 2
MFM 2P U2L6 Graphing Linear Relations March 07, 2013 Example 3. The yearbook costs $5000 up front for set up and consultation fees. It costs $10 on top of that to print each book. Make a table to model the cost of a yearbook for up to 400 ordered books. Graph it. What is the slope, what is the y intercept? Homework Page 143 #1, 3, 5, 7 10, 12