Slope and Equation Challenges 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 connecting these two points?

• 1

• 0.5

• 2

• 3

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

• y = 2x + 3

• y = -\frac{2}{3}x + 4

• y = -rac{3}{2}x + 2

• y = rac{3}{2}x - 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 (y) based on hours rented (x).

• y = 2x - 10

• y = 5x + 10

• y = 2x + 10

• y = 10x + 2

4. Find the slope of the line that passes through the points (1, 2) and (4, 5). What does this slope represent in a real-world context?

• The slope of the line is 1.

• The slope of the line is 2.

• The slope of the line is -1.

• The slope of the line is 0.

5. The line representing the temperature in degrees Fahrenheit (y) over time in hours (x) is given by the equation y = 3x + 15. What is the slope, and what does it indicate about the temperature change?

• The slope is 3, indicating the temperature increases by 3 degrees Fahrenheit per hour.

• The slope is 5, indicating the temperature increases by 5 degrees Fahrenheit per hour.

• The slope is 3, indicating the temperature remains constant over time.

• The slope is 15, indicating the temperature decreases by 15 degrees Fahrenheit per hour.

6. Convert the equation 4x - 2y = 8 into slope-intercept form and identify the slope and y-intercept.

• Slope: 1, Y-intercept: -2

• Slope: -2, Y-intercept: 4

• Slope: 2, Y-intercept: -4

• Slope: 0, Y-intercept: 8

7. A school is planning to build a new playground. The cost (y) can be modeled by the equation y = 500 + 150x, where x is the number of swings. What is the slope, and what does it represent?

• The slope is 300, representing the cost decrease per swing.

• The slope is 150, representing the cost increase per swing.

• The slope is 500, representing the total cost of the playground.

• The slope is 150, representing the total number of swings.

8. Calculate the slope of the line that passes through the points (3, 4) and (7, 10). How would you interpret this slope in a practical scenario?

• 3.0

• 1.5

• 2.0

• 0.5

9. The equation of a line is given as y - 2 = 5(x - 1). Convert this to slope-intercept form and identify the slope and y-intercept.

• Slope: 5, Y-intercept: -3

• Slope: 3, Y-intercept: -1

• Slope: 0, Y-intercept: 2

• Slope: 2, Y-intercept: 1