Linear Function Word Problems

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 dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

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 write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation (y = mx + b).

Front

If a ticket costs $5 and a total of $290 is made, how do you find the number of tickets sold?

Back

Set up the equation: 5x + 55 = 290, where x is the number of tickets. Solve for x to find the number of tickets sold.

Front

What is the fixed fee in a ticket sales problem?

Back

The fixed fee is a constant amount added to the total cost regardless of the number of tickets purchased.

Front

How do you determine the cost of multiple items with a fixed fee?

Back

Use the equation: Total Cost = (Cost per item * Number of items) + Fixed fee.

Front

In a problem involving multiple items, how do you set up an equation?

Back

Identify the cost of each item, the number of items, and any additional fees. Then, create an equation that represents the total cost.

Front

What is the total cost if 50 shirts are ordered at $8 each with a $15 setup fee?

Back

Total Cost = 8(50) + 15 = 415.

Front

How do you solve for an unknown in a linear equation?

Back

Isolate the variable on one side of the equation using algebraic operations to find its value.