Linear Equations 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 it mean to solve a word problem involving linear equations?

Back

Solving a word problem involving linear equations means translating a real-world situation into a mathematical equation and finding the unknown variable.

Front

How do you set up a linear equation from a word problem?

Back

Identify the variables, write an equation based on the relationships described in the problem, and include any constants.

Front

What is the slope 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 find the number of items you can buy with a budget?

Back

Set up an equation where the total cost of items equals the budget. Solve for the number of items.

Front

If a problem states that 'each item costs a certain amount', how do you express this in an equation?

Back

Multiply the number of items (n) by the cost per item (c) to express the total cost: Total Cost = n * c.

Front

What is a constant in a linear equation?

Back

A constant is a fixed value that does not change. In the equation y = mx + b, b is the constant.

Front

How do you determine the total cost of multiple items with different prices?

Back

Set up an equation that adds the costs of each item multiplied by the quantity purchased.

Front

What is the formula to calculate the total cost of a service with a base fee and a variable fee?

Back

Total Cost = Base Fee + (Variable Fee per unit * Number of units used).