Exploring Slopes and Y-Intercepts in Linear Contexts

A car travels from point A (2, 3) to point B (6, 7). What is the slope of the line connecting these two points?

• 2

• 0.5

• 3

• 1

Using the points from the previous question, find the y-intercept of the line. What does this represent in the context of the car's journey?

• The y-intercept indicates the car's maximum speed during the journey.

• The y-intercept represents the total distance traveled by the car.

• The y-intercept is the initial position of the car at the start of its journey.

• The y-intercept shows the time taken to reach the destination.

A store sells 3 shirts for $30 and 5 shirts for $50. Determine the slope of the line that represents the cost of shirts based on the number purchased.

• 15

• 20

• 25

• 10

Using the points from the previous question, find the y-intercept. What does this value indicate about the cost when no shirts are purchased?

• The y-intercept indicates the variable cost per shirt sold.

• The y-intercept shows the maximum number of shirts that can be purchased.

• The y-intercept represents the total cost of all shirts purchased.

• The y-intercept indicates the fixed cost when no shirts are purchased.

Two friends are walking in parallel paths. Friend A walks from point (1, 2) to point (4, 5) and Friend B walks from point (1, 4) to point (4, 7). Are their paths parallel? Explain your reasoning.

• Yes, but they are not straight paths.

• No, Friend A walks faster than Friend B.

• Yes, their paths are parallel.

• No, their paths intersect.

If the slope of a line is 2, what would be the equation of a line parallel to it that passes through the point (3, 1)?

• y = -2x + 7

• y = 2x - 5

• y = 2x - 3

• y = 2x + 1

A bike rental shop charges a flat fee of $10 plus $2 per hour. If another shop charges $5 plus $3 per hour, find the points where their costs are equal. What does this mean?

• The costs are equal at 3 hours, where both shops charge $16.

• The costs are equal at 4 hours, where one shop charges $18 and the other $22.

• The costs are equal at 6 hours, where both shops charge $25.

• The costs are equal at 5 hours, where both shops charge $20.

Using the points from the previous question, determine the slope of the line representing the first shop's pricing. What does this slope indicate?

• The slope represents the total cost of the items.

• The slope indicates the fixed price of the shop's products.

• The slope indicates the rate of change in price with respect to quantity.

• The slope shows the average price of all items sold.

A gardener plants flowers in a straight line. The first flower is planted at (0, 1) and the second at (4, 5). Write the equation of the line representing the flower bed. What does the y-intercept represent?

• y = 2x + 1; y-intercept = 2

• y = 3x + 1; y-intercept = 1

• y = x + 1; y-intercept = 1

• y = x - 1; y-intercept = -1

If another gardener plants flowers in a line parallel to the first, starting at (0, 3), what would be the equation of this new line?

• y = mx + 5

• y = 2x + 3

• y = mx + 3

• y = mx - 3