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 steep the line is.

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 rate of change (slope), and the starting value (y-intercept) to form the equation in the form y = mx + b.

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

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

Back

In this equation, 10 represents the monthly fee, and 3 represents the cost per visit.

Front

How do you determine the total cost of hiring a mechanic who charges a flat fee and an hourly rate?

Back

The total cost can be expressed as y = hourly rate * hours + flat fee.

Front

If a plant grows at a rate of 3 cm per month, how would you express its height after x months?

Back

y = 3x + 5, where y is the height of the plant and x is the number of months.

Front

What is the equation to model the amount of gasoline remaining in a tank after t hours if it starts with 19 gallons and uses 3 gallons per hour?

Back

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

Front

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

Back

The constant term (b) represents the y-intercept, which is the value of y when x is 0.