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 'slope' 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 is the y-intercept 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 involving a flat fee and a variable cost?

Back

Identify the flat fee as the y-intercept and the variable cost as the slope. The equation will be in the form y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you identify the slope and y-intercept from a word problem?

Back

Look for the constant amount (flat fee) for the y-intercept and the rate of change (cost per hour/item) for the slope.

Front

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

Back

The coefficients represent the relationship between the variables. The coefficient of x (slope) shows how much y changes for a unit change in x.

Front

How can you represent a situation with two different items in a linear equation?

Back

Use the standard form Ax + By = C, where A and B are the prices of the items, and C is the total amount spent.

Front

What is an example of a linear equation from a word problem?

Back

If a plumber charges $25 for a service call and $50 per hour, the equation is y = 50x + 25, where y is the total cost and x is the number of hours.

Front

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

Back

Identify the quantities involved, assign variables, and express the relationships using an equation.