Linear 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 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 represents the starting point of the line on the y-axis.

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 Sonya has $40 and spends $2 each day, how can we express her remaining money after x days?

Back

y = -2x + 40, where y is the amount of money left.

Front

What is the total cost equation for downloading songs if the startup cost is $7.95 and each song costs $0.95?

Back

Total cost (y) = 0.95x + 7.95, where x is the number of songs downloaded.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations.

Front

What does it mean to model a situation with a linear equation?

Back

Modeling a situation with a linear equation means creating a mathematical representation of a real-world scenario to analyze and solve it.

Front

In the equation y = -30x + 100, what does the -30 represent?

Back

The -30 represents the rate at which the man is descending, indicating he goes down 30 feet per minute.

Front

How can you find the number of dogs washed if 6 cats were washed and the total earnings were $60?

Back

Set up the equation: 5(6) + 7.5d = 60, where d is the number of dogs washed. Solve for d to find 4 dogs.