Linear Equations Verbal Flashcard

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 is the y-intercept in a linear equation?

Back

The y-intercept 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 fixed costs (y-intercept) and the variable costs (slope) based on the context of the problem, then formulate the equation.

Front

What is the total cost equation for a gym membership that costs $50 per month plus a $100 enrollment fee?

Back

C = 50m + 100, where C is the total cost and m is the number of months.

Front

What is the total cost equation for a taxi that charges $5 plus $2.50 per mile?

Back

y = 2.50x + 5, where y is the total cost and x is the number of miles.

Front

What is the total cost equation for a car rental that charges $50 plus $0.30 per mile?

Back

y = 0.30x + 50, where y is the total cost and x is the number of miles driven.

Front

What is the total cost equation for shipping that charges $10 plus $1.50 per pound?

Back

y = 1.50x + 10, where y is the total cost and x is the weight in pounds.

Front

What is the total cost equation for a water park that charges $30 plus $5 per ride?

Back

y = 5x + 30, where y is the total cost and x is the number of rides.

Front

What is the significance of the fixed cost in a linear equation?

Back

The fixed cost is the initial amount that does not change regardless of the quantity consumed or used. It is represented by the y-intercept in the equation.