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 of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

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

If a plumber charges $50 for a house call and $25 per hour, how would you express the total cost (C) for h hours of labor?

Back

C = 50 + 25h.

Front

What is the equation for a service that charges a flat fee plus a variable cost per unit?

Back

The equation is C = flat fee + (variable cost per unit * number of units).

Front

How do you find the total cost if you know the fixed and variable costs?

Back

Add the fixed cost to the product of the variable cost per unit and the number of units used.

Front

What is the equation for Juanita's cell phone bill if she uses x minutes?

Back

C = 15 + 0.20x.

Front

How do you determine the total cost for towing a vehicle if the service charges a flat fee plus a per mile charge?

Back

Use the equation C = flat fee + (cost per mile * number of miles).

Front

If Scott's Automotive charges $35 plus $7 per hour, how would you express the total charge (T) for x hours?

Back

T = 35 + 7x.