Linear Equations from Words

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 an 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 Sandra has a $20 iTunes gift card and spends $3 each month, what is the equation for her remaining balance after x months?

Back

y = -3x + 20

Front

What does the equation y = -3x + 20 represent in Sandra's situation?

Back

It represents that for every month (x), Sandra spends $3, reducing her initial balance of $20.

Front

What is the equation for the total cost C to rent a paddle boat for h hours if there is a $15 deposit and $2 per hour?

Back

C = 2h + 15

Front

How can you identify the y-intercept from a situation?

Back

Look for the initial value or starting amount before any changes occur.

Front

If Bob saves $40 per month starting with $150, what is the equation for his savings after x months?

Back

y = 40x + 150

Front

What does the equation y = 40x + 150 represent in Bob's savings situation?

Back

It indicates that Bob's savings increase by $40 for each month (x) he saves, starting from $150.