Writing Linear Equations from 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 (m) represent in a linear equation?

Back

The slope (m) 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 (b) represent in a linear equation?

Back

The y-intercept (b) 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

In the equation y = 2x + 15, what does the 2 represent?

Back

The 2 represents the slope, indicating that for every 1 unit increase in x, y increases by 2 units.

Front

In the equation y = 20x + 100, what does the 100 represent?

Back

The 100 represents the initial amount or starting value of y when x is 0.

Front

Write the linear equation for a situation where a person saves $50 per month starting with $200.

Back

y = 50x + 200

Front

Write the linear equation for a situation where a car rental company charges a flat fee of $30 plus $10 per hour.

Back

y = 10x + 30

Front

If a gym membership costs $25 per month plus a one-time fee of $50, what is the equation?

Back

y = 25x + 50

Front

What is the equation for a situation where a person earns $15 per hour and has a starting salary of $200?

Back

y = 15x + 200