Writing Linear Equations from Word Problems

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 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 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.

Front

What is the equation for a service charge plus hourly rate?

Back

y = mx + b, where y is the total cost, m is the hourly rate, x is the number of hours, and b is the initial service charge.

Front

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

Back

x represents the independent variable, and y represents the dependent variable.

Front

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

Back

Coefficients indicate the strength and direction of the relationship between the variables. The coefficient of x (slope) shows how much y changes for a unit change in x.

Front

How do you identify the total cost in a word problem involving multiple items?

Back

Set up an equation that combines the costs of each item, typically in the form Ax + By = C, where A and B are the costs, x and y are the quantities, and C is the total cost.

Front

What is the first step in solving a word problem that involves a linear equation?

Back

Read the problem carefully to identify the key information, including the quantities involved and their relationships.

Front

How do you convert a word problem into a linear equation?

Back

Translate the words into mathematical symbols, using variables for unknowns and constants for known values.