Slope and Intercept: Word Problems for 8th Grade Math

1. A car travels from point A (2, 3) to point B (6, 7). What is the slope of the line that represents the car's path?

• 2

• 1

• 3

• 0.5

2. The equation of a line is given in standard form as 2x + 3y = 12. Convert this equation to slope-intercept form.

• y = 2x + 6

• y = -3/2x + 2

• y = 3/2x - 4

• y = -2/3x + 4

3. A bike rental shop charges a flat fee of $10 plus $2 per hour. Write the equation in slope-intercept form that represents the total cost (C) as a function of hours (h).

• C = 10h + 2

• C = 2h + 10

• C = 5h + 10

• C = 10 + 2h^2

4. A student scores 70 points on their first test and 90 points on their second test after studying for 3 hours. Calculate the slope of the line that represents the relationship between study hours and test scores.

• 8.00

• 7.50

• 6.67

• 5.00

5. The line representing the temperature in a city over time is given by the equation y = 4x + 15. What does the slope represent in this context?

• The slope indicates the initial temperature at time zero.

• The slope represents the rate of change of temperature over time, specifically an increase of 4 degrees for each unit of time.

• The slope represents the maximum temperature reached in the city.

• The slope shows the total temperature over the entire time period.

6. Convert the equation 5x - 2y = 10 into slope-intercept form and identify the slope and y-intercept.

• Slope: 2/5, Y-intercept: 5

• Slope: 0, Y-intercept: -2

• Slope: 5/2, Y-intercept: -5

• Slope: -5/2, Y-intercept: 10

7. A gardener plants flowers in a straight line. If the first flower is planted at (1, 2) and the second at (4, 5), what is the slope of the line representing the row of flowers?

• 2

• 0.5

• 3

• 1

8. The cost of a concert ticket is represented by the equation C = 25 + 5n, where n is the number of tickets purchased. What is the slope and what does it represent?

• The slope is 5, representing the additional cost per ticket.

• The slope is 25, representing the total cost of tickets.

• The slope is 10, representing the cost of parking at the concert.

• The slope is 5, representing the cost of refreshments per ticket.

9. A train travels from station A at (0, 0) to station B at (10, 20). Calculate the slope of the train's path and interpret its meaning in terms of speed.

• The slope of the train's path is 0.

• The slope of the train's path is 1.

• The slope of the train's path is 2.

• The slope of the train's path is 5.

10. The equation of a line is given as y - 4 = 3(x - 2). Convert this to slope-intercept form and identify the slope.

• The slope is 3.

• The slope is 2.

• The slope is 4.

• The slope is -3.