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 (m) represent in a linear equation?

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 does the y-intercept (b) represent 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 an equation for a word problem involving a fixed charge and a variable charge?

Back

Identify the fixed charge and the variable charge, then write the equation in the form: Total Cost = Fixed Charge + (Variable Charge per unit * Number of units).

Front

If a service charges a flat fee plus a rate per hour, how would you represent this in an equation?

Back

Let y be the total cost, x be the number of hours, and c be the flat fee. The equation would be: y = rate * x + c.

Front

What is the equation for Scott's Automotive if Kylie was charged $63?

Back

7x + 35 = 63, where x is the number of hours.

Front

How do you determine the total cost of a cell phone bill based on usage?

Back

The total cost (C) can be calculated using the equation: C = monthly fee + (cost per minute * number of minutes used).

Front

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

Back

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

Front

What does the equation y = -25x + 120 represent in a real-world scenario?

Back

It represents a situation where there are initially 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

How do you model a situation where membership increases over time?

Back

Use the equation: y = increase rate * x + initial members, where y is the total membership, x is the number of months.