Writing Linear Equations from Situations

Jacob conducts an egg-drop experiment. He drops it from 32 feet in the air and it falls at 4 feet per minute. Write a linear equation to represent this situation.

• y = -4x+32

• y = 32x+4

• y = -4x+8

• y = -8x+32

A mechanic charges an initial fee of $75 plus an hourly fee of $50. Write the equation for the situation.

Mathematical Equivalence

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An airplane is 30,000 feet above ground and descends at the rate of 2,000 feet per minute. Write a linear equation to represent this situation.

• y = 2,000x-30,000

• y = -2,000x+15

• y = -30,000x+15

• y = -2,000x+30,000

Michael has $650 in his savings account. He withdraws $50 each week. Write a linear equation to represent the relationship between the weeks and the total money left in his savings account.

• y = -650x+50

• y = -50x+650

• y = 13x + 50

• y = -13x+650

Lisa saves $20 every week. If she already has $200 in her savings account, write a linear equation to represent the total amount of money in her savings account after x weeks.

• y = 20x + 200

• y = 200x + 20

• y = -20x + 200

• y = 20x - 200

A balloon is released and rises at a steady rate of 100 feet per minute. If the balloon starts at a height of 50 feet, write a linear equation to represent the height of the balloon after x minutes.

• y = 100x + 50

• y = 50x + 100

• y = -100x + 50

• y = 100x - 50

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

• y = 20x + 5

• y = 5x +20

• y=-5x + 20

• y = 5x - 20

Suppose that a bike rents for $4 plus $1.50 per hour. Write an equation in slope-intercept form that models this situation.

• y = 4x + 1.50

• y = 1.50x + 4

• y = -4x +1.50

• y = 4x - 1.50

An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the situation.

• y = - 2,000x + 30,000

• y = - 2,000x - 30,000

• y = 30,000x + 2,000

• y = -30,000x + 2,000

Talk Time Phone Company charges $0.12 per minute of phone use plus a monthly service fee of $8.00 for its phone service. Which equation below can be used to find c, the total cost for one month when m, minutes are used?

• c = 0.12m + 8m

• m = 0.12c + 8

• c = 0.12m + 8

• c = 0.20m