Writing 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 (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 relationship between them, and express that relationship in the form of a linear equation.

Front

What is the equation for total cost (C) if there is a fixed fee and a variable fee per hour (h)?

Back

C = fixed fee + (variable fee per hour * h).

Front

If a plumber charges $25 for a house call and $120 per hour, how would you express the total cost (C) for h hours?

Back

C = 120h + 25.

Front

How do you determine the equation from a situation where a quantity increases at a constant rate?

Back

Use the formula y = mx + b, where m is the rate of increase and b is the initial quantity.

Front

What is the equation for a situation where a tank releases water at a constant rate?

Back

If there are 120 gallons initially and it releases water at 25 gallons per minute, the equation is y = -25x + 120.

Front

How do you model a situation with a startup fee and a monthly fee?

Back

Use the equation y = monthly fee * x + startup fee.

Front

What is the equation for Juanita's cell phone bill if she pays a monthly fee and a per-minute charge?

Back

C = 15 + 0.20x, where C is the total cost and x is the number of minutes used.