Linear Equation 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 slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept 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 an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and translate the words into a mathematical equation.

Front

What is the equation for a fitness club membership that starts with 80 members and increases by 15 each month?

Back

y = 15x + 80, where y is the total membership and x is the number of months.

Front

How do you represent a situation where a man descends from a height at a constant rate?

Back

Use a linear equation like y = -30x + 100, where y is the height and x is the time in minutes.

Front

What is the equation for a taxi fare that includes a flat fee and a per-mile charge?

Back

y = 0.75x + 3, where y is the total fare, x is the number of miles, and 3 is the flat fee.

Front

How do you write an equation for a camp fee that charges a base fee plus an additional amount for each extra child?

Back

y = 225x + 625, where y is the total fee, x is the number of additional children, and 625 is the base fee.

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

It represents a situation where there are 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

What is the first step in solving a linear equation word problem?

Back

Identify the variables and what they represent in the context of the problem.