Writing Linear Equations in Context

Front

What is a linear equation?

Back

A linear equation is an equation that models a relationship between two variables with a constant rate of change, typically represented in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you interpret the y-intercept in a linear equation?

Back

The y-intercept represents the value of the dependent variable when the independent variable is zero. It indicates the starting point of the relationship modeled by the equation.

Front

What is the slope in a linear equation, and what does it represent?

Back

The slope (m) in a linear equation represents the rate of change of the dependent variable with respect to the independent variable. It indicates how much the dependent variable changes for a one-unit increase in the independent variable.

Front

How can you write a linear equation from a word problem?

Back

To write a linear equation from a word problem, identify the variables, determine the relationship between them, and express that relationship in the form of an equation.

Front

What does the equation G = 19 - 3t represent in the context of Jill's road trip?

Back

This equation models the amount of gasoline (G) remaining in Jill's tank after t hours, starting with 19 gallons and using 3 gallons per hour.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope using the formula m = (y2 - y1) / (x2 - x1), then use one of the points and the slope to write the equation in point-slope form, and convert it to slope-intercept form if needed.

Front

What is the significance of the original height of a candle in a linear model?

Back

The original height of the candle is represented by the y-intercept of the linear equation that models the candle's height over time.

Front

How do you derive a linear equation from a table of values?

Back

To derive a linear equation from a table of values, identify the change in the dependent variable (y) for each unit change in the independent variable (x) to find the slope, then use a point from the table to write the equation.

Front

What is the formula to convert Celsius to Fahrenheit?

Back

The formula to convert Celsius (C) to Fahrenheit (F) is F = (9/5)C + 32.

Front

What does the equation S = 120.25 - 5.75d represent in Margaret's soap usage?

Back

This equation models the amount of soap (S) remaining after d days of use, starting with 120.25 grams and using 5.75 grams per day.