Mastering Slope and Line Equations for Grade 8

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?

• 0.5

• 1

• 3

• 2

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 for each hour rented. Write the equation in slope-intercept form that represents the total cost (C) as a function of hours rented (h).

• C = 2h + 10

• C = 2h - 10

• C = 5h + 10

• C = 10h + 2

5. A school is planning to build a new playground. The cost (C) in thousands of dollars can be modeled by the equation C = 5x + 20, where x is the number of months until completion. What is the slope and what does it indicate?

• The slope is 10, indicating a cost increase of 10 thousand dollars per month.

• The slope is 5, indicating a cost increase of 5 thousand dollars per month.

• The slope is 5, indicating a cost decrease of 5 thousand dollars per month.

• The slope is 20, indicating a cost increase of 20 thousand dollars per month.

6. Convert the equation 4y - 8x = 16 into slope-intercept form and identify the slope and y-intercept.

• Slope: 0, Y-intercept: 16

• Slope: 1, Y-intercept: 2

• Slope: -2, Y-intercept: 8

• Slope: 2, Y-intercept: 4

7. A line passes through the points (3, 4) and (7, 10). Calculate the slope and write the equation of the line in slope-intercept form.

• y = -1x + 5

• y = 0.5x + 3

• y = 2x + 1

• y = 1.5x - 0.5

8. The temperature in a city increases by 3 degrees every hour. If the initial temperature is 15 degrees, write the equation in slope-intercept form that represents the temperature (T) after h hours.

• T = 3h + 15

• T = 15h + 3

• T = 3h - 15

• T = 2h + 15

9. 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) as a function of the number of notebooks (n).

• C = 5n + 10

• C = 3n + 5

• C = 5n + 3

• C = 3n - 5

10. The line representing the distance (d) a runner has covered over time (t) is given by the equation d = 2t + 5. What is the slope and what does it represent in this scenario?

• The slope is 5, representing the runner's speed of 5 units of distance per unit of time.

• The slope is 2, representing the runner's speed of 2 units of distance per hour.

• The slope is 0, indicating the runner is stationary.

• The slope is 2, representing the runner's speed of 2 units of distance per unit of time.