Analyzing Slopes and Intercepts in Function Relationships

A graph shows the relationship between hours studied and test scores. If the slope of the line is 5, what does this indicate about the relationship?

• The relationship indicates that more hours studied leads to higher test scores, specifically an increase of 5 points per hour.

• An increase of 5 hours studied results in a decrease of 5 points in test scores.

• The relationship shows no correlation between hours studied and test scores.

• The slope of 5 indicates that test scores decrease by 5 points for each hour studied.

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. If the graph of this relationship is a line, what are the slope and y-intercept?

• Slope: 0.25, Y-intercept: 30

• Slope: 0.50, Y-intercept: 20

• Slope: 1.00, Y-intercept: 10

• Slope: 0.75, Y-intercept: 15

The graph of a plant's growth over time is a curve that levels off. What type of function might this represent, and what does the slope indicate about growth?

• Logistic function; slope indicates decreasing growth rate as resources are limited.

• Quadratic function; slope indicates growth that accelerates indefinitely.

• Linear function; slope indicates rapid growth as resources increase.

• Exponential function; slope indicates constant growth rate.

A store's revenue can be modeled by the equation R = 50x, where x is the number of items sold. What type of function is this, and what does the slope represent?

• The function is linear, and the slope represents the total cost per item sold.

• The function is quadratic, and the slope represents the total revenue.

• The function is linear, and the slope represents the revenue generated per item sold, which is $50.

• The function is exponential, and the slope represents the number of items sold.

A line on a graph shows the distance traveled by a cyclist over time. If the line has a negative slope, what does this tell you about the cyclist's movement?

• The cyclist is resting and not moving.

• The cyclist is moving backward or returning.

• The cyclist is accelerating forward.

• The cyclist is moving at a constant speed.

A graph shows the temperature change throughout the day. If the y-intercept is 15 degrees Celsius, what does this represent in the context of the problem?

• The maximum temperature reached during the day is 15 degrees Celsius.

• The temperature at noon is 15 degrees Celsius.

• The temperature at sunset is 15 degrees Celsius.

• The initial temperature at the start of the day is 15 degrees Celsius.

A student graphed the number of books read over several months. If the graph is a straight line with a slope of 2, how many books does the student read per month?

• 4 books per month

• 2 books per month

• 3 books per month

• 1 book per month

A graph shows the relationship between the number of hours worked and the amount earned. If the line crosses the y-axis at $100, what does this represent?

• It shows that $100 is the maximum amount that can be earned.

• It represents a fixed payment of $100 when no hours are worked.

• It represents the total earnings after working 10 hours.

• It indicates a bonus of $100 for every hour worked.

A scientist plots the population of a species over time and finds a linear relationship. If the slope is 3, what does this indicate about the population growth?

• The population grows by 3 units per time unit.

• The population decreases by 3 units per time unit.

• The population grows by 3 units every 5 time units.

• The population remains constant over time.