Writing Linear Equations from Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that models 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 does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It represents 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.

Front

In the equation y = mx + b, what do x and y represent?

Back

In the equation y = mx + b, x represents the independent variable, and y represents the dependent variable.

Front

What is the fixed cost in a linear equation representing a service charge?

Back

The fixed cost is the constant term (b) in the equation, representing the initial charge before any variable costs are added.

Front

How do you identify the variable cost in a service charge equation?

Back

The variable cost is the coefficient of x (m) in the equation, representing the cost that changes based on the number of services provided.

Front

Write the equation for a service that charges a flat fee plus a variable rate per hour.

Back

y = mx + b, where m is the variable rate per hour and b is the flat fee.

Front

If a service charges $50 plus $20 per hour, what is the equation?

Back

y = 20x + 50.

Front

What is the equation for a service that charges $30 per hour and a $10 service fee?

Back

y = 30x + 10.