Mastering Slope, Intercepts, and Real-World Algebra

1. A line passes through the points (2, 3) and (4, 7). What is the slope of the line?

• 1

• 3

• 4

• 2

2. The equation of a line is given as y = 2x + 5. What are the y-intercept and the slope of this line?

• Slope: 2, Y-intercept: 5

• Slope: 3, Y-intercept: 5

• Slope: 2, Y-intercept: 0

• Slope: 5, Y-intercept: 2

3. Sarah buys 3 notebooks and 2 pens for a total of $12. If each notebook costs $3, how much does each pen cost?

• $3.50

• 1.50

• $2.00

• $4.00

4. A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write an equation to represent the total cost (C) in terms of miles driven (m). What is the slope?

• C = 20 + 0.75m; slope = 0.75

• C = 20 + 0.50m; slope = 0.50

• C = 15 + 0.50m; slope = 0.50

• C = 20 + 0.25m; slope = 0.25

5. The perimeter of a rectangular garden is 48 meters. If the length is 2 meters more than twice the width, find the dimensions of the garden using algebra.

• Width: 8 meters, Length: 16 meters

• Width: 10 meters, Length: 18 meters

• Width: 5 meters, Length: 20 meters

• Width: 7.33 meters, Length: 16.67 meters

6. A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys 4 pencils and some erasers for a total of $5.50, how many erasers did the student buy?

• 5

• 4

• 3

• 2

7. The equation of a line is y = -3x + 4. What is the slope and what does it tell you about the line?

• The slope is -3, indicating the line decreases as x increases.

• The slope is -4, indicating the line is horizontal.

• The slope is 3, indicating the line increases as x increases.

• The slope is 0, indicating the line decreases as x increases.

8. A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make 4 batches of the recipe, how much of each ingredient do you need? Use the distributive property to solve.

• 6 cups of flour and 9 cups of sugar

• 4 cups of flour and 6 cups of sugar

• 10 cups of flour and 15 cups of sugar

• 8 cups of flour and 12 cups of sugar

9. A bike rental shop charges a one-time fee of $15 plus $2 for each hour rented. Write an equation for the total cost (C) in terms of hours (h) and find the slope.

• C = 15 + 3h; slope = 3

• C = 10 + 2h; slope = 2

• C = 15 + 2h; slope = 2

• C = 15 + h; slope = 1

10. If a line has a slope of 5 and passes through the point (1, 2), what is the equation of the line in slope-intercept form?

• y = 5x - 3

• y = 2x + 5

• y = 5x + 2

• y = 5x - 1