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 f(x) = 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 of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you interpret the equation y = mx + b?

Back

In the equation y = mx + b, m represents the slope of the line, and b represents the y-intercept. This equation describes a linear relationship between x and y.

Front

What does the function g(x) = 3x + 4 represent in a real-world context?

Back

The function g(x) = 3x + 4 represents the total cost of purchasing x packages of bubble gum, where each package costs $3 and there is a fixed cost of $4.

Front

If Derek works for 4 hours, how much does he earn according to the function d(x) = 9.25x?

Back

Derek earns $37 after working for 4 hours, as calculated by d(4) = 9.25 * 4.

Front

What is the meaning of the function f(x) = 9x + 5?

Back

The function f(x) = 9x + 5 represents a linear relationship where for every hour worked, $9 is earned, plus an additional $5.

Front

How do you find the value of a function at a specific point, such as g(8)?

Back

To find the value of a function at a specific point, substitute the value of x into the function. For g(8), calculate g(8) = 3(8) + 4.

Front

What does the equation y = 68 - x represent in terms of temperature?

Back

The equation y = 68 - x represents the change in temperature over time, where y is the temperature in Fahrenheit and x is the time in hours.

Front

How do you interpret the result of a function, such as f(7) = 68?

Back

The result f(7) = 68 means that when the input x is 7, the output of the function is 68, indicating the value of the dependent variable.