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 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 does the y-intercept in a linear equation represent?

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 a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

In the equation y = 25x + 40, what do the numbers 25 and 40 represent?

Back

In this equation, 25 represents the cost per hour (slope), and 40 represents the fixed service fee (y-intercept).

Front

What is the equation for a situation where a fixed fee is added to a variable cost?

Back

The equation is y = mx + b, where m is the variable cost per unit, and b is the fixed fee.

Front

If a man is climbing down from 100 feet at a rate of 30 feet per minute, how would you express this situation as a linear equation?

Back

The equation is y = 100 - 30x, where y is the height after x minutes.

Front

How do you determine the total cost in a situation with a base fee and a variable cost?

Back

Add the base fee to the product of the variable cost per unit and the number of units: Total Cost = Base Fee + (Variable Cost per Unit * Number of Units).

Front

What is the equation for Connor's lemonade stand if he starts with 15 cups and sells 5 more cups per hour?

Back

The equation is y = 5x + 15, where y is the total number of cups sold after x hours.

Front

What does the term 'variable cost' mean in a linear equation context?

Back

Variable cost refers to the cost that changes with the level of output or activity, represented by the slope in a linear equation.