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 represent in a linear equation?

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 is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you identify the slope from a word problem?

Back

The slope can be identified as the rate of change described in the problem, often expressed in units per time (e.g., meters per minute, dollars per week).

Front

Write the linear equation for a situation where a person saves $15 every week starting with $100.

Back

y = 15x + 100

Front

What does x typically represent in a linear equation derived from a word problem?

Back

In many word problems, x represents the independent variable, often time (e.g., minutes, weeks) or another quantity that changes.

Front

If a train descends at a rate of 50 meters per minute, what is the slope of the linear equation representing its height over time?

Back

The slope is -50, indicating a decrease in height.

Front

In the equation y = -4x + 32, what does the 32 represent?

Back

The 32 represents the initial height from which the object is dropped, or the y-intercept.

Front

How do you convert a word problem into a linear equation?

Back

Identify the variables, determine the rate of change (slope), and find the initial value (y-intercept) to form the equation y = mx + b.

Front

What is the significance of the negative slope in a linear equation?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.