Front

What does the function P(x) = 8600 − 22x represent in the context of a small business?

Back

P(x) represents the weekly profit of the business, where x is the number of hours worked by the employee.

Front

How do you solve the equation 2x + 2y = 6 for y?

Back

To solve for y, isolate y: 2y = 6 - 2x, then y = -x + 3.

Front

What is the function rule for a linear function with a slope of 2 and a y-intercept of 3?

Back

The function rule is y = 2x + 3.

Front

What is the definition of a y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, typically representing a relationship between two variables.

Front

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

Back

The slope indicates the rate of change of the function; it shows how much y changes for a unit change in x.

Front

How can you determine the profit from the function P(x) = 8600 − 22x when x = 10?

Back

Substitute x = 10 into the function: P(10) = 8600 - 22(10) = 8600 - 220 = 8380.

Front

What does it mean for a function to be linear?

Back

A linear function is one that graphs to a straight line, characterized by a constant rate of change (slope).

Front

How do you find the x-intercept of a linear equation?

Back

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

Front

What is the general form of a linear equation?

Back

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