3.4. Slope Intercept Form The Leaky Bottle. My Notes ACTIVITY
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1 Slope Intercept Form SUGGESTED LEARNING STRATEGIES: Use Manipulatives, Create Representations, Discussion Group, Think/Pair/Share, Activating Prior Knowledge Owen s water bottle leaked in his bookbag. He did the following eperiment to find how quickl water drains from a small hole placed in a water bottle.. Follow the steps below and fill in the table. Get a water bottle and a container to catch the water. Poke a small hole in the bottom of the water bottle Ensure the hole is facing down, and open the bottle cap. Draw a line on the bottle ever 5 seconds to mark the water level. After the water is drained from the bottle, measure the heights at each of the times that ou marked. Time in Seconds Height of Water (cm). Make a scatter plot of the data on the grid below. M Notes ACTIVITY. College Board. All rights reserved. Height of Water Time. Does the relationship between time and the height of the water appear to be linear? Eplain our reasoning.. Is the data ou collected continuous or discrete? Eplain our reasoning. 5. Draw a line through the points on the scatterplot ou created. a. Find the slope of the line ou drew. b. Find the -intercept of the line ou drew. MATH TERMS The -intercept of a line is the -value when =. It is the place where the line crosses the -ais. Unit Equations and the Coordinate Plane 5
2 ACTIVITY. Slope Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Group Presentation, Think/Pair/Share, Create Representations. Write an equation that gives the height of the water H given the time t. 7. How does the coefficient of t in our equation relate to the eperiment? Be certain to include appropriate units in our answer.. How does the constant term in the equation relate to the eperiment? Be certain to include appropriate units in our answer. 9. For each linear equation below: Make a table of values. Graph using a different color for each line. Determine the slope. a. = b. = c. = = = = College Board. All rights reserved. SpringBoard Mathematics with Meaning TM Level
3 Slope Intercept Form ACTIVITY. SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Create Representations, Look for a Pattern. How does the slope ou found for each linear equation relate to the coefficients of in the equations for Question 9? M Notes. For each linear equation below: Make a table of values. Graph using a different color for each line. Determine the slope. 5 5 College Board. All rights reserved. a. = - b. = - c. = - = = = How does the slope ou found relate to the coefficients of in the equations for Question?. Write an equation of a line that is: a. Steeper (increasing) than the ones ou graphed in Question 9. b. Steeper (decreasing) than the ones ou graphed in Question. Unit Equations and the Coordinate Plane 7
4 ACTIVITY. Slope Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Look for a Pattern, Group Presentation, Think/Pair/Share, Guess and Check. For each linear equation below: Make a table of values. Graph using a different color for each line. Determine the slope. 5 5 a. = b. = c. = 5 College Board. All rights reserved. 5. Compare and contrast the slopes ou found in Questions 9,, and. Refer to the representations ou ve created in our comparisons. What conclusions can ou draw about the slope of lines?. Write the equation of a line that is steeper than but less than one. SpringBoard Mathematics with Meaning TM Level
5 Slope Intercept Form ACTIVITY. SUGGESTED LEARNING STRATEGIES: Create Representations, Look for a Pattern, Think/Pair/Share 7. For each linear equation below: Make a table of values. Graph using a different color for each line. Determine the -intercept. Determine the slope. M Notes 5 5 a. = + b. = + c. = -. How is the -intercept related to the constant term in the equations? College Board. All rights reserved. 9. Look at the lines ou graphed in item 7. a. How do the three lines appear to be related? b. Look at the three equations and make a conjecture based on our answer to part a. c. What would happen to the graph of = - if it were shifted units up? d. What would happen to the graph of = + if it were shifted 9 units down?. Identif the slope and -intercept in each of the following equations. a. = + 5 b. = - + c. = - Unit Equations and the Coordinate Plane 9
6 ACTIVITY. Slope Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Shared Reading, Interactive Word Wall, Discussion Group, Create Representations. Identif and plot the -intercept of the equation = + on the coordinate grid and use the slope to find two more points on the line. MATH TERMS The slope-intercept form of a linear equation is = m + b, where m is the slope and b is the -intercept.. Sketch a line through the three points. Equations of the form = m + b are written in slope-intercept form, where m is the slope of the line, and b is the -intercept of the line.. Use the -intercept and the slope to graph the following equations of lines. a. = - b. = - + c. = - + College Board. All rights reserved. 5 SpringBoard Mathematics with Meaning TM Level
7 Slope Intercept Form ACTIVITY. SUGGESTED LEARNING STRATEGIES: Work Backwards, Quickwrite, Group Presentation. Owen found that the equation = - + represented the water leaking from his bottle. M Notes a. What is the -intercept, and what would it represent in this contet? b. What is the slope, and what would it represent in this contet? c. Eplain to Owen what would have to happen to the bottle for the slope to change to -. College Board. All rights reserved. 5. Eplain how to graph the equation = - without using a table of values.. The table and the equation below represent different functions = - Which function has the greater rate of change? How do ou know? Unit Equations and the Coordinate Plane 5
8 ACTIVITY. Slope Intercept Form CHECK YOUR UNDERSTANDING Write our answers on notebook paper. Show our work.. Find the slope..5 7 Graph the linear equations.. =. = -5. = - 5. Write an equation of a line that has a slope that is greater than but less than.. Write the equation of the line graphed below. Graph the linear equations. 7. = +. = = - 5. Write an equation for the line graphed below.. Write the equation of a function with a greater rate of change than the function graphed in item.. MATHEMATICAL REFLECTION Eplain two was to graph a linear equation of the form = m + b, where m and b represent an real number. College Board. All rights reserved. 5 SpringBoard Mathematics with Meaning TM Level
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1. Given the function f (x) = x 2 3bx + (c + 2), determine the values of b and c such that f (1) = 0 and f (3) = 0.
Chapter Review IB Questions 1. Given the function f () = 3b + (c + ), determine the values of b and c such that f = 0 and f = 0. (Total 4 marks). Consider the function ƒ : 3 5 + k. (a) Write down ƒ ().