Point-Slope Equations and Slope from Points Quiz

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation in point-slope form that represents the total cost (C) based on the number of miles driven (m) if you start with 50 dollars for 0 miles.

• C - 50 = 0.20(m + 0)

• C = 50 + 0.20m

• C - 50 = 0.20(m - 0)

• C - 50 = 0.10(m - 0)

Two friends, Alex and Jamie, are walking in a park. Alex walks at a speed of 3 feet per minute, while Jamie walks at a speed of 5 feet per minute. If they start walking together at the same point, write the equation in point-slope form for the distance each has walked after t minutes.

• d_A = 2t, d_J = 4t

• d_A = 5t, d_J = 3t

• d_A = 3t, d_J = 5t

• d_A = 3t, d_J = 6t

A gardener is planting flowers in a straight line. If the first flower is planted at the coordinate (2, 3) and the second flower at (5, 7), find the slope and write the equation in point-slope form for the line of flowers.

• y - 3 = (4/3)(x - 2)

• y - 3 = (2/5)(x - 2)

• y - 3 = (5/2)(x - 2)

• y - 3 = (3/4)(x - 2)

A bike shop sells bikes for $200 each and offers a discount of $20 for every bike purchased. Write the equation in point-slope form that represents the total cost (C) based on the number of bikes (b) purchased, starting from the cost of 200 for 1 bike.

• C - 200 = -10(b - 1)

• C - 200 = -20(b - 1)

• C - 200 = -20(b + 1)

• C - 200 = -20b

A student is saving money for a new laptop. She saves $15 each week, starting with $30. Write the equation in point-slope form that represents her total savings (S) after w weeks.

• S - 30 = 15(w - 0)

• S - 30 = 15(w + 1)

• S = 15w + 30

• S - 30 = 10(w - 0)

A train travels from Station A to Station B, covering a distance of 120 miles in 2 hours. Write the equation in point-slope form that represents the distance (D) traveled over time (t) if the train starts at 0 miles at 0 hours.

• D = 120t

• D = 60t + 10

• D = 60t

• D = 30t

A restaurant's daily sales can be modeled by the points (1, 150) and (4, 300). Calculate the slope and write the equation in point-slope form for the sales (S) based on the number of days (d) since opening.

• S - 150 = 100(d - 1)

• S - 150 = 50(d - 1)

• S - 150 = 25(d - 1)

• S - 150 = 75(d - 1)

A swimming pool is being filled at a rate of 10 gallons per minute. If it starts with 50 gallons, write the equation in point-slope form that represents the total volume of water (V) in the pool after t minutes.

• V - 50 = 10(t - 0)

• V - 50 = 5(t - 0)

• V = 10t + 50

• V - 50 = 10(t + 1)

A delivery service charges a base fee of $25 plus $5 for each package delivered. Write the equation in point-slope form that represents the total charge (C) based on the number of packages (p) delivered, starting from 25 dollars for 0 packages.

• C = 5p + 30

• C - 30 = 5(p - 1)

• C - 25 = 10(p - 0)

• C - 25 = 5(p - 0)

A photographer charges a sitting fee of $100 and $25 for each photo taken. Write the equation in point-slope form that represents the total cost (C) based on the number of photos (p) taken, starting from 100 dollars for 0 photos.

• C - 100 = 25(p - 0)

• C = 25p + 100

• C - 100 = 50(p - 0)

• C - 100 = 15(p - 0)