Understanding Linear Equations in Real-Life Scenarios
Explore the concept of linear equations through real-life examples involving distance, speed, time, and constant rates. Practice solving problems to determine distances covered, areas mowed, and volumes of water coming out of a faucet over specific periods. Engage in workshops and assessments to reinforce learning and apply linear equations in context.
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LINEAR EQUATIONS Eureka Math 8thGrade Module 4 Topic B
LESSON 10 Notes, examples(2), workshop
Notes Distance, speed, time Average speed is found by dividing the total distance the total time. d =rt r =d t =d t r Where d = distance, t = time, and r = rate or speed
Example 1 Paul walks 2 miles in 25 minutes. How far can he walk in 137.5 minutes?
Example 2 Dave lives 15 miles from town A. He is driving at a constant speed of 50 miles per hour from his home away from (in the opposite direction of) the city. How far away is Dave from the town after ? hours of driving? Using your equation, how far from town is he after 1 hour?
Workshop Must Do May Do Exponents retest Complete Topic A assessment Lesson 10 cw #1-3 Khan academy Exponents review If tested out of exponents: Crossing the River/Carnival Bears Start Homework
LESSON 11 Examples(2), workshop
Example 1 Pauline mows a lawn at a constant rate. Suppose she mows a 35 sq. ft. lawn in 2.5 minutes. What area can she mow in 10 minutes? t minutes? (time in minutes) Linear Equation: (area in square feet)
Example 2 Water flows at a constant rate out of a faucet. Suppose the volume of water that comes out in 3 minutes is 10.5 gallons. How many gallons come out in t minutes? (time in minutes) Linear Equation: (in gallons)
Workshop Must Do May Do Finish lesson 10 cw #1-3 Lesson 11 cw #1-3 Khan academy Exponents review Topic A assessment corrections If tested out of exponents: Crossing River/Carnival Bears Inky puzzles Integer games
LESSON 12 Warm up, example, notes, workshop
Warm Up Emily tells you that she scored 32 points in a basketball game. Write down all the possible ways she could have scores 32 with only two- and three-point baskets. Use the table to organize your work. If x is the number of two- pointers and y is the number of three-pointers, what equation can we write for the total?
Standard Form of Linear Equations A linear equation in the form: Where A, B, and C represent set numbers, and x and y represent variables or unknowns. + = Ax By C A solution to this equation is an ordered pair (x, y), that makes the equation true. To find solutions, you pick a set number for x or y, substitute, and then solve for the other value.
Slope-Intercept Form of Linear Equations A linear equation in the form: Where m and b represent set numbers, and x and y represent variables or unknowns. = + y mx b m is the constant rate of change (slope) b is the y-intercept (crosses y-axis) (x, y) are solutions that make the equation true
Converting Standard to Slope-Intercept + = -Ax Ax Ax -Ax By BB By C = C + C Ax Ax C = = y B B A C = + y x B B
+ = Example 50 15 x y Choose x-values Let x = 5 Substitute: Solve for y: Choose y-values Let y = 10 Substitute: Solve for x: + = 50 ) 5 ( 15 y + = 50 10 15 x + = 50 10 -10 -10 50 = x (-50) (-50) 5 = 15 x + = 50 ) 5 ( 250 +250 +250 15 15 y + = y 5 = 265 y 1 = x (5, 265) is a solution 50 10 1 10, 10) is a solution (
Workshop Must Do May Do Finish lesson 10&11 cw Exit ticket 10 & 11 Lesson 12 cw #1-5 HINTS: think about why #1-2 small numbers easier! #3 choose y, solve for x #4 choose x that are multiples of 5 Khan academy Inky puzzles
LESSON 13 Discussion/example, workshop
Example 5 1 1 4 2 2 3 -1 -2 7 8
Workshop Must Do May Do Finish lesson 12 cw HINTS: think about why #1-2 small numbers easier! #3 choose y, solve for x #4 choose x that are multiples of 5 Lesson 13 cw #1-3 Khan academy Folder organize Notes sheet
LESSON 14 Explore, discussion/notes, workshop (part2)
Explore Complete Lesson 14 classwork #1-3 and #7-9 SKIP #4-6 and #10-12 FOR NOW Prepare to discuss #3 and #9
Notes When in standard form Ax + By = C: An equation with A=1 and B=0 (in other words: 1x + 0y = C or x = C) will be a vertical line through (C, 0) An equation with A=0 and B=1 (in other words 0x + 1y = C or y = C) will be a horizontal line through (0, C)
Workshop Must Do May Do Finish lesson 12&13 cw Exit ticket 12 & 13 Lesson 14 cw #1-12 #4-6 #10-12 Khan academy Complete all cw & hw Folder organize Notes sheet
