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 of a linear function represents the rate of change of the function. It indicates how much the dependent variable (y) changes for a unit change in the independent variable (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 is represented by the value of b in the equation y = mx + b.

Front

How do you find the cost of multiple items using a linear function?

Back

To find the cost of multiple items, use the equation y = mx + b, where m is the cost per item, x is the number of items, and b is any fixed cost.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation of the line is y = 2x + 3.

Front

If a function is represented as y = 4x + 1, what is the value of y when x = 5?

Back

When x = 5, y = 4(5) + 1 = 20 + 1 = 21.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

How can you determine the cost of 50 shirts if each shirt costs $8 and there is a $15 setup fee?

Back

Using the equation y = 8x + 15, where x = 50, y = 8(50) + 15 = 400 + 15 = 415.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you identify the x-intercept of a linear function?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.