Math 1: Algebra, Geometry and Statistics Ms. Sheppard-Brick
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1 Exit Ticket 32 Chapter 3 Quiz 3 Review Students Will Be Able To: Determine whether the slope of a line is positive, negative, zero, or undefined Find the slope of a line between two points. Find the slope of a line given the graph. Find the rate of change from a graph. Use rate of change to solve problems. Determine whether three points are collinear. Given two points, find another point on the line between them. Review Skill: Write an equation for a direct variation word problem or an inverse variation word problem. Reference Information: Given two points, A (x!, y! ) and B (x!, y! ), the slope of the line between A and B is: m A, B = y! y! x! x! To find the slope of a line shown on a graph: o Find and mark two integer- value points on the line o Follow the grid lines to create a right triangle with the line as the hypotenuse. o Calculate using slope =!"#$!"# o Always simplify your fractions fully Three points A, B, and C are collinear if and only if: m A, B = m B, C = m(a, C) Rate of change on a distance- time graph is average speed, which is equal to the slope of the line between two points. Direct Variation equations take the form y = cx, where c is a constant. When reading a graph from left to write, a line with a positive slope goes up, and a line with a negative slope goes down. Horizontal lines have a slope of zero, and vertical lines have an undefined slope. 1
2 CORE 1. Determine whether the slope of each line shown is positive, negative, zero or undefined. Write +,, 0, or. a. b. c. d. e. f. g. h. 2. Find the slope between each pair of points. Show your work and remember to simplify your fractions. a. ( 6, 3) and ( 4, 9) b. 2, 6 and 8, 2 c. ( 6, 3) and (1, 3) d. 1, 2 and 1, 6 e. (0, 8) and (3, 12) f. (7, 1) and (7, 8) 2
3 3. Find the slope of each of the lines graphed below. Show your work and simplify your answers. a. b. c. d. e. f. 3
4 4. The graph below shows total caffeine consumed over time. Over the course of the morning, Cassandra has a double shot of espresso (lots of caffeine), a cup of tea (medium amount of caffeine) and a cup of decaf coffee (very little caffeine). a. Between which two points is Cassandra drinking decaf coffee? How can you tell? b. Between which two points is Cassandra drinking espresso? How can you tell? c. Find the rate of caffeine consumed between points D and E. Show your work. d. Find the rate of caffeine consumed between points F and G. Show your work. e. Find the rate of the caffeine consumed over the entire morning. Show your work. 4
5 5. Determine whether each set of three points is collinear. Show your work and justify your answer in writing. a. A 4, 6, B (0, 3) and C (4, 0) b. D ( 8, 8), E ( 3, 7) and F (1, 6) 6. Given each pair of points, find one other point that is on the same line. Use the graph. a. Find a point on the line through G ( 3, 2) and H 3, 2. b. Find a point on the line through J ( 1, 2) and K ( 1, 5). 5
6 7. Darnell earns $12 per hour at his job at Newbury Comics. a. If Darnell works 5 hours, how much money does he earn? b. If Darnell works 8 hours, how much money does he earn? c. If Darnell earns $108, how many hours did he work? d. Let h = the number of hours Darnell works and let m = the total amount of money he earns. Write an equation for Darnell s total pay in terms of the number of hours he works. EXTENSION 8. Joanne has twelve chocolate bars to distribute among her students. a. If she has 2 students, how many chocolate bars does each student get? b. If she has 6 students, how many chocolate bars does each student get? c. If each student gets 3 chocolate bars, how many students were there? d. Let c = the number of chocolate bars each student gets and let s = the number of students. Write an equation for the relationship between s and c. 6
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