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 variable 'x' typically represent in word problems involving linear equations?

Back

In word problems, 'x' often represents the quantity of an item or the number of units being considered.

Front

What does the variable 'y' typically represent in word problems involving linear equations?

Back

In word problems, 'y' usually represents the total cost, total amount, or another dependent variable that changes based on 'x'.

Front

How do you write a linear equation from a word problem?

Back

Identify the quantities involved, assign variables, determine the relationship between them, and express that relationship as an equation.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

In the equation 4x + 8y = 45, what do the coefficients 4 and 8 represent?

Back

The coefficients 4 and 8 represent the cost per unit of the items being purchased (e.g., soda and pizza) in the context of the problem.

Front

How can you determine the total cost from a linear equation?

Back

By substituting the value of 'x' (the number of units) into the equation and solving for 'y' (the total cost).

Front

What does it mean if a linear equation has no solution?

Back

It means that there is no combination of values for the variables that satisfies the equation, often represented by parallel lines on a graph.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of 'y' when 'x' is zero.

Front

How do you interpret the slope of a linear equation in a real-world context?

Back

The slope represents the rate of change between the two variables, indicating how much 'y' changes for a unit change in 'x'.