Linear Equation 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 of a linear equation represent?

Back

The slope 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 represents the starting point of the line on the y-axis.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept often represents a fixed cost or initial amount before any variable costs are added.

Front

What is the general form of a linear inequality?

Back

A linear inequality is similar to a linear equation but uses inequality signs (>, <, ≥, ≤) instead of an equal sign.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through the points.

Front

What does it mean if a linear equation has a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How can you write an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and translate the words into a mathematical equation.

Front

What is the significance of the initial fee in a cost equation?

Back

The initial fee represents a fixed cost that must be paid regardless of the number of items produced or services used.