Writing Linear Equations from Context

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 value of the dependent variable.

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

If a candle burns at a rate of 2 inches per hour, how would you express the height of the candle after x hours?

Back

y = -2x + 12, where y is the height of the candle and x is the time in hours.

Front

Amelia saves $20 per week starting with $100. Write the equation for her savings after x weeks.

Back

y = 20x + 100, where y is the total savings and x is the number of weeks.

Front

What does the equation y = 3x + 10 represent in the context of gym membership?

Back

In this equation, 10 is the monthly fee (y-intercept) and 3 is the cost per visit (slope).

Front

How do you model the remaining gasoline in a tank after t hours if the tank holds 19 gallons and uses 3 gallons per hour?

Back

G = 19 - 3t, where G is the amount of gasoline remaining.

Front

What is the total cost equation for Bob's Plumbing service?

Back

y = 25x + 40, where y is the total cost, x is the number of hours worked, and 40 is the service fee.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term (y-intercept) indicates the initial value of the dependent variable when the independent variable is zero.