Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the value of a linear function at a specific point?

Back

To find the value of a linear function at a specific point, substitute the x-value into the function and solve for y.

Front

What is the equation of a line that starts at 48 bottles and decreases by 5 bottles per day?

Back

y = 48 - 5x.

Front

If a gym charges a startup fee of $40 and $10 per month, what is the equation for total cost after x months?

Back

y = 10x + 40.

Front

What does the term 'initial value' refer to in a linear function?

Back

The initial value refers to the y-intercept, which is the starting value of the function when x is 0.

Front

How can you represent a situation where an amusement park charges $20 to enter and $1.50 per ride?

Back

The equation is y = 1.5x + 20, where y is the total cost and x is the number of rides.

Front

What is the significance of the negative slope in a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficient of x (slope) indicates the rate of change, while the constant term (y-intercept) indicates the starting value.