Linear Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be expressed in 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 one-unit increase in 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 write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express it in the form y = mx + b.

Front

If a waitress earns a base salary plus a percentage of her tips, how can this be modeled as a linear function?

Back

The total earnings can be modeled as M = 0.75t + 100, where M is the total earnings, t is the total tips, and 0.75 represents the percentage of tips kept.

Front

What is the equation for the total cost of renting a paddle boat if there is a fixed fee and a variable fee?

Back

C = 2h + 15, where C is the total cost, h is the number of hours rented, 2 is the cost per hour, and 15 is the fixed deposit fee.

Front

How do you calculate the total cost after applying a discount?

Back

Subtract the discount from the original price. For example, if the original price is $6.50 per dozen and the discount is $1.50, the new price is $6.50 - $1.50.

Front

What changes to a linear function occur when the starting point and rate of change are modified?

Back

The starting point changes the y-intercept, and the rate of change modifies the slope. For example, increasing the starting height and changing the falling speed alters the equation.

Front

How can you model savings over time with a linear function?

Back

Savings can be modeled as y = 40x + 150, where y is the total savings, x is the number of months, 40 is the amount saved per month, and 150 is the initial amount.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients indicate the slope and y-intercept of the line. The slope shows the rate of change, while the y-intercept shows the starting value.