Linear Equation 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the average rate of serving people in a word problem?

Back

To find the average rate, divide the total time taken by the number of people served. For example, if it takes 12 minutes to serve 2 people, the average rate is 12 minutes / 2 people = 6 minutes per person.

Front

What is the formula to calculate the cost of lessons based on the number of lessons taken?

Back

The cost can be calculated using a linear equation in the form of C = mx + b, where C is the total cost, m is the cost per lesson, x is the number of lessons, and b is any fixed cost.

Front

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

Back

Identify the variables, write an equation based on the relationships described in the problem, and include any constants. For example, if pumpkins are sold for $5 each and tomatoes for $3 each, the equation would represent total sales.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change between the two variables in the equation. It indicates how much one variable changes for a unit change in the other variable.

Front

How can you represent a situation with two variables using a system of equations?

Back

You can represent a situation with two variables by creating two equations that describe the relationships between the variables. For example, if p is the number of plants and t is the number of trees, you can write p + t = total number of plants and trees.

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. It represents the value of the dependent variable when the independent variable is zero.

Front

How do you determine the number of days food will last based on a linear equation?

Back

You can determine the number of days by setting up an equation that represents the total amount of food divided by the daily consumption. For example, if you start with 250 pounds and consume 12 pounds per day, the equation would be 250 - 12x = 0.

Front

What is the relationship between the coefficients in a linear equation and the context of a word problem?

Back

The coefficients in a linear equation represent the rates or costs associated with the variables in the context of the problem. For example, in a cost equation, the coefficient represents the cost per unit.

Front

How do you solve a linear equation for one variable?

Back

To solve a linear equation for one variable, isolate the variable on one side of the equation by performing inverse operations on both sides.