SlopeIntercept Form Word Problems Focus 7 Learning Goal

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. 4 3 2 1 0 In addition to level 3. 0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas. The student will demonstrate and explain the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. The student will demonstrate and identify proportional relationships, lines, and linear equations and use functions to model quantities. With help from the teacher, the student has partial success with level 2 and 3 elements. Even with help, students have no success with level 2 and 3 content.

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.

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 = 20 x + b What is the one time charge? Substitute that number in for “b. ” y = 20 x + 50 This is the equation that models this situation.

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. 25 x + b What is the one time charge? Substitute that number in for “b. ” y = 0. 25 x + 30 This is the equation that models this situation.

Renting a Moving Van… Use the equation you wrote about the moving van and complete table. y = 0. 25 x + 30 Miles (x) 25 50 75 100 Cost (y) 36. 25 42. 50 48. 75 55. 00 y = 0. 25(25) + 30 y = 6. 25 + 30 y = 0. 25(75) + 30 y = 18. 75 + 30 y = 0. 25(50) + 30 y = 12. 50 + 30 y = 0. 25(100) + 30 y = 25 + 30 y = 36. 25 y = 42. 50 y = 48. 75 y = 55. 00

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 = 8 x + b What is the one time charge? Substitute that number in for “b. ” y = 8 x + 70 This is the equation that models this situation.

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 y = = 8 x + 70 8(15) + 70 120 + 70 190 The cost for 15 months of singing lessons is $190.