Real World Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What do independent and dependent variables represent in a linear equation?

Back

The independent variable is the variable that is changed or controlled in a mathematical model, while the dependent variable is the variable that is affected by the independent variable.

Front

In the context of a job, what do x and y typically represent?

Back

In job-related scenarios, x often represents the number of items (like pizzas delivered), and y represents the total earnings or money made.

Front

How do you determine the slope of a linear equation?

Back

The slope (m) of a linear equation is determined by the ratio of the change in y (vertical change) to the change in x (horizontal change) between two points on the line.

Front

What is the 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 is 0.

Front

How can 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.

Front

What does the equation y = 48 - 5x represent in a real-world context?

Back

This equation represents the number of bottles left after drinking 5 bottles per day from an initial 48 bottles.

Front

How do you calculate total earnings from a job with a base pay and a variable pay per item?

Back

Total earnings can be calculated using the formula: Total Earnings = Base Pay + (Pay per Item * Number of Items Delivered).

Front

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

Back

Coefficients represent the rate of change of the dependent variable with respect to the independent variable.

Front

How do you solve for a variable in a linear equation?

Back

To solve for a variable, isolate it on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division.