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Slope-Intercept Form Word Problems

Slope-Intercept Form Word Problems. Focus 7 - Learning Goal #1: The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. What is Slope-Intercept Form of an Equation?. y = m x + b

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Slope-Intercept Form Word Problems

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  1. Slope-Intercept Form Word Problems

  2. Focus 7 - Learning Goal #1:The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities.

  3. What is Slope-Intercept Form of an Equation? • y = mx + b • The equation includes the slope “m” and the y-intercept “b”. • The slope is the repeating amount or the rate of change. • The y-intercept is the starting amount.

  4. Working out at the gym… • In order to become a member at a local gym, there is a $50 start up fee then it costs $20 per month. Write an equation in slope-intercept form modeling this situation. • Start with the format y = mx + b. • What is the repeating amount in this problem? • Substitute that number in for “m.” • y = 20x + b • What is the one time charge? • Substitute that number in for “b.” • y = 20x + 50 • This is the equation that models this situation.

  5. Renting a Moving Van… • A rental company charges a flat fee of $30 to rent a moving van plus $0.25 per mile. Write an equation in slope-intercept form modeling this situation. • Start with the format y = mx + b. • What is the repeating amount in this problem? • Substitute that number in for “m.” • y = 0.25x + b • What is the one time charge? • Substitute that number in for “b.” • y = 0.25x + 30 • This is the equation that models this situation.

  6. Renting a Moving Van… Use the equation you wrote about the moving van and complete table. y = 0.25x + 30 36.25 48.75 55.00 42.50 y = 0.25(75) + 30 y = 18.75 + 30 y = 48.75 y = 0.25(100) + 30 y = 25 + 30 y = 55.00 y = 0.25(25) + 30 y = 6.25 + 30 y = 36.25 y = 0.25(50) + 30 y = 12.50 + 30 y = 42.50

  7. Time to sing… • In order to join a singing club, there is a $70 startup fee and a $8 monthly fee every month. Write an equation in slope-intercept form modeling this situation. • Start with the format y = mx + b. • What is the repeating amount in this problem? • Substitute that number in for “m.” • y = 8x + b • What is the one time charge? • Substitute that number in for “b.” • y = 8x + 70 • This is the equation that models this situation.

  8. Time to sing… Use the equation you wrote about belonging to the singing club to find out the total cost for 15 months of club membership. y = 8x + 70 y = 8(15) + 70 y = 120 + 70 y = 190 The cost for 15 months of singing lessons is $190.

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