Point-Slope Form: Real-World Slope Interpretations

A car is traveling at a speed of 60 miles per hour. If the car starts at a point (0, 0) and travels for 2 hours, what is the equation in point-slope form that represents the car's distance from the starting point?

• y = 30x

• y = 120x

• y = 60x + 10

• y = 60x

A gardener plants a tree at the point (1, 3) and observes that it grows at a rate of 2 inches per year. Write the equation in point-slope form that represents the height of the tree after 't' years.

• y - 3 = 3(t - 1)

• y - 3 = 2(t + 1)

• y = 2t + 1

• y - 3 = 2(t - 1)

A cyclist starts at the point (0, 5) and rides downhill at a slope of -3. What is the equation in point-slope form that represents the cyclist's height after 'x' miles ridden?

• y - 5 = -3(x - 0)

• y - 5 = -1(x - 0)

• y = -3x + 5

• y - 5 = 3(x - 0)

A student scores 75 points on their first test and increases their score by 5 points for each subsequent test. Write the equation in point-slope form that represents the student's score after 'n' tests.

• y - 75 = 5n

• y - 75 = 10(n - 1)

• y - 75 = 5(n - 1)

• y = 75 + 5n

A train leaves the station at a speed of 50 miles per hour from the point (0, 0). If it travels for 3 hours, what is the equation in point-slope form that represents the distance traveled?

• y = 50x + 10

• y = 30x

• y = 100x

• y = 50x

A basketball player scores 10 points in the first quarter and increases their scoring rate by 4 points each quarter. Write the equation in point-slope form that represents the total points scored after 'q' quarters.

• y = 10 + 4q

• y - 10 = 2(q - 1)

• y - 10 = 5(q - 1)

• y - 10 = 4(q - 1)

A hiker starts at a height of 100 feet and climbs at a rate of 10 feet per hour. Write the equation in point-slope form that represents the hiker's height after 'h' hours.

• y - 100 = 10h

• y = 10h + 100

• y - 100 = 5(h - 0)

• y - 100 = 10(h - 0)

A factory produces 200 units of a product in the first month and increases production by 50 units each month. Write the equation in point-slope form that represents the total production after 'm' months.

• y - 200 = 25(m - 1)

• y - 200 = 50(m + 1)

• y = 50m + 200

• y - 200 = 50(m - 1)

A swimmer starts at a depth of 5 meters and dives deeper at a rate of -2 meters per minute. Write the equation in point-slope form that represents the swimmer's depth after 't' minutes.

• y - 5 = -2t

• y = -2t + 5

• y + 2 = -5t

• y + 5 = -2t

A student starts with a score of 80 on their first assignment and improves by 3 points for each subsequent assignment. Write the equation in point-slope form that represents the student's score after 'a' assignments.

• y - 80 = 2(a - 1)

• y - 80 = 3(a + 1)

• y - 80 = 4(a - 1)

• y - 80 = 3(a - 1)