Mastering Slope: Word Problems and Calculations

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

• 3

• 0.5

• 1

• 2

2. If the slope of a line is 2 and it passes through the point (1, 4), what is the y-intercept of the line?

• 2

• 1

• 3

• 4

3. A bike rental shop charges a flat fee of $10 plus $2 per hour. Write the equation in slope-intercept form and identify the slope and y-intercept.

• y = 2x - 10; slope = 2, y-intercept = -10

• y = 2x + 10; slope = 2, y-intercept = 10

• y = 10x + 2; slope = 10, y-intercept = 2

• y = 5x + 10; slope = 5, y-intercept = 10

4. Two friends start a lemonade stand. Friend A sells 5 cups for $10, and Friend B sells 8 cups for $16. Calculate the slope of their earnings and analyze who has a better rate of earnings per cup.

• Friend A earns $1.50 per cup.

• Both friends have the same rate of earnings per cup, which is $2.

• Friend B earns $2.50 per cup.

• Friend A sells 5 cups for $15.

5. A student scores 80 on their first test and 90 on their second test. If the scores are plotted on a graph, what is the slope of the line connecting these two points?

• 10

• 20

• 15

• 5

6. A gardener plants flowers in a straight line. If the first flower is planted at (0, 1) and the second at (4, 5), what is the slope of the line representing the row of flowers?

• 2

• 0.5

• -1

• 1

7. A delivery truck travels from point C (3, 5) to point D (7, 9). What does the slope tell you about the truck's speed?

• The slope of 1 shows the truck is at a standstill.

• The slope of 1 indicates the truck is speeding up.

• The slope of 1 means the truck is moving backwards.

• The slope of 1 indicates a consistent speed.

8. If a line has a slope of -3 and passes through the point (2, 6), what is the equation of the line in slope-intercept form?

• y = -3x + 6

• y = 3x + 6

• y = -3x + 12

• y = -3x - 12

9. A restaurant's revenue increased from $2000 to $3000 over 5 months. Calculate the slope of the revenue line and interpret what this means for the restaurant's growth.

• $150 per month

• $250 per month

• $300 per month

• $200 per month

10. A train travels from station X (1, 2) to station Y (5, 10). What is the slope of the line, and what does it indicate about the train's speed over that distance?

• The slope of the line is 2.

• The slope of the line is 3.

• The slope of the line is 0.5.

• The slope of the line is 1.