Writing Linear Equations from Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form Ax + By = C, where A, B, and C are constants.

Front

What does the slope of a linear equation represent in a real-world context?

Back

The slope represents the rate of change between the two variables in the equation, indicating how one variable changes in relation to another.

Front

How do you identify the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. In the equation y = mx + b, b represents the y-intercept.

Front

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

Back

The x-intercept is the value of x when y is 0. It indicates where the line crosses the x-axis.

Front

How can you represent a word problem as a linear equation?

Back

Identify the quantities involved, assign variables to them, and express the relationships between these quantities using an equation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B are not both zero.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the values of the variables that make the equation true.

Front

How do you determine the total score from correct and incorrect answers in a test scenario?

Back

Use the equation: Total Score = (Points per correct answer * Number of correct answers) - (Points lost per incorrect answer * Number of incorrect answers).

Front

What is the formula for writing a linear equation based on a rate of change?

Back

The formula is y = mx + b, where m is the rate of change (slope) and b is the initial value (y-intercept).

Front

How do you set up an equation for a situation involving multiple items with different prices?

Back

Assign variables to each item, multiply the price of each item by its corresponding variable, and set the sum equal to the total spent.