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 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 represents the starting point of the line on 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

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

How do you find the base rate in a word problem involving costs?

Back

Set up a system of equations based on the given information and solve for the base rate.

Front

What is the total cost equation for renting a paddle boat with a $15 deposit and $2 per hour?

Back

C = 2h + 15, where C is the total cost and h is the number of hours.

Front

If Alex is losing weight at a rate of 2 pounds per week, how do you express his weight after a certain number of weeks?

Back

Weight = Initial weight - (2 pounds/week * number of weeks).

Front

How do you determine how many weeks it will take to reach a target weight?

Back

Set up an equation based on the rate of weight loss and solve for the number of weeks needed to reach the target weight.