Writing Linear Equations from 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

What does the slope in a linear equation represent?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) 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 a linear equation from a word problem?

Back

Identify the variables, determine the fixed costs and variable costs, and then formulate the equation based on the relationship described in the problem.

Front

In the equation y = mx + b, what do m and b represent?

Back

In the equation, m represents the slope of the line, and b represents the y-intercept.

Front

What is the fixed cost in a word problem involving a rental service?

Back

The fixed cost is the amount charged regardless of usage, such as a base fee for renting a car.

Front

What is a variable cost in a word problem involving a rental service?

Back

The variable cost is the amount charged based on usage, such as a per-mile charge for driving a rental car.

Front

How would you represent the total cost of a service that has a fixed fee and a variable fee?

Back

The total cost can be represented as y = fixed fee + (variable rate * number of units used).

Front

If a rental company charges $150 per week plus $0.10 per mile, what is the equation for total cost over 2 weeks?

Back

y = 2(150) + 0.10x, where x is the number of miles driven.

Front

What is the equation for Bob's Plumbing service charge?

Back

y = 15x + 40, where y is the total charge, x is the number of hours worked.