Linear Equation Application 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 steep the line is.

Front

What is the y-intercept (b) in a linear equation?

Back

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

Front

How do you find the total cost after a startup fee and a monthly fee?

Back

To find the total cost, use the equation y = startup fee + (monthly fee * number of months).

Front

If you save $15 each week starting with $10, how do you express the total savings after w weeks?

Back

The total savings can be expressed as y = 10 + 15w.

Front

What is the equation for a subscription service with a one-time fee and a monthly fee?

Back

The equation is y = one-time fee + (monthly fee * number of months).

Front

In the equation y = mx + b, what does x represent?

Back

In the equation y = mx + b, x represents the independent variable, which is the input value.

Front

How do you solve for the number of weeks needed to save a certain amount?

Back

Rearrange the savings equation to isolate w: w = (total savings - initial amount) / savings per week.

Front

What is the total cost of a service with a $30 startup fee and $12 monthly fee for 8 months?

Back

Total cost = 30 + (12 * 8) = $126.

Front

What is the equation for a club membership with a $30 startup fee and $4 monthly fee?

Back

The equation is y = 4m + 30, where m is the number of months.