Slope and Equation Challenges for 8th Graders

1. A car travels from a point (2, 3) to (5, 9). What is the slope of the line that represents the car's path?

• 1

• 4

• 3

• 2

2. Using the slope from the previous question, write the equation of the line in slope-intercept form, given that it passes through the point (2, 3).

• y = 2x + 3, where 2 is the slope and 3 is the y-intercept.

• y = 3x + 2, where 3 is the slope and 2 is the y-intercept.

• y = mx + b, where m is the slope and b is the y-intercept.

• y = b + mx, where b is the slope and m is the y-intercept.

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

• C = 2h + 10

• C = 10 + 2h^2

• C = 2h - 10

• C = 10h + 2

4. If a line passes through the points (1, 2) and (4, 8), calculate the slope and write the equation in slope-intercept form.

• y = 0.5x + 2

• y = 2x

• y = x + 1

• y = 3x

5. A gardener plants flowers in a straight line, starting at the point (0, 1) and reaching (3, 7). What is the slope of the line, and what is the equation in slope-intercept form?

• Slope: 2, Equation: y = 2x + 1

• Slope: 2, Equation: y = 2x - 1

• Slope: 1, Equation: y = x + 1

• Slope: 3, Equation: y = 3x + 1

6. A student scores 70 points on their first test and increases their score by 5 points for each subsequent test. Write the equation in slope-intercept form for the student's score (S) based on the number of tests taken (t).

• S = 70t + 5

• S = 5t + 75

• S = 5t + 70

• S = 10t + 60

7. A train travels from station A at (0, 0) to station B at (6, 12). Calculate the slope and write the equation in slope-intercept form for the train's journey.

• y = 2x

• y = 4x - 2

• y = x + 6

• y = 3x

8. A store sells notebooks for $3 each and charges a $5 service fee. Write the equation in slope-intercept form that represents the total cost (C) for buying n notebooks.

• C = 8n + 5

• C = 5n + 3

• C = 3n + 5

• C = 3n - 5

9. A line passes through the points (2, 4) and (6, 10). Find the slope and write the equation in slope-intercept form.

• y = 2x + 2

• y = 4x - 4

• y = (3/2)x + 1

• y = (1/2)x + 3

10. A swimming pool is filled with water at a rate of 4 gallons per minute, starting from an empty pool. Write the equation in slope-intercept form that represents the volume of water (V) in gallons after t minutes.

• V = 2t

• V = 10t

• V = 4t + 10

• V = 4t