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9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 1/13 Exercises Lesson 1: Alternate Forms of an Equation of a Line 1. Given the following graph, what is the equation of the line in: a. point-slope form b. slope- -intercept form c. form 2. Determine the slope and intercept of the line . 3. A line has a slope of and passes through the point . a. Write the equation of the line in point-slope form. b. Using your equation from part a) determine three additional points that lie on the line. 4. A line is represented by the equation . Rewrite the equation in the form and . 5. Determine the value of such that the line represented by the equation has a -intercept of and then rewrite the equation of the line in the form .

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 2/13 6. At C, g of carbon dioxide has a volume of L. For each degree the temperature, , increases, the volume, , of the carbon dioxide increases by . a. Write an equation that represents the relationship between the volume of the g of the carbon dioxide gas and temperature in point-slope form. b. What is the volume of the g of the carbon dioxide at C? 7. Determine if the following lines represent a partial or direct variation. a. b. c. 8. A line is represented by the equation . a. Determine the equation of a line that is parallel to the given line. b. Determine the equation of a line that is perpendicular to the given line. c. Determine the values of slope that would result in a line that is steeper than the given line. Lesson 2: Comparing Linear and Non-Linear Relations 1. Determine if the following graphs represent a linear or non-linear relation.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 3/13 a. b. c.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 4/13 d. 2. Determine if the following tables of values represent a linear or non-linear relation. a. b. c.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 5/13 3. Determine if the following equations represent a linear or non-linear relation. a. b. c. d. 4. Determine which of the following equations does NOT represent a linear relation. a. b. c. d. 5. Hyacinth says that is linear because she believes the degree on the variables and is one. Kody disagrees and shows Hyacinth that the graph of the relation is not a straight line. Rewrite the equation so that Hyacinth can clearly see that the degree on all of the variables is not equal to one. 6. To calculate the volume of a cylinder we can use the formula , where represents the radius and represents the height. a. A cylinder has a ±xed height of units. Is the relationship between volume and radius linear or non-linear? b. A cylinder has a ±xed radius of units. Is the relationship between volume and height linear or non-linear?

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