Writing Linear Equations - 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 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What does 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the value of y when x is 0.

Front

How do you write an equation from a word problem?

Back

To write an equation from a word problem, identify the variables, determine the relationship between them, and express that relationship mathematically.

Front

What is the equation for the total cost of a holiday meal for x people if it costs $12.50 per person plus a $30 delivery fee?

Back

y = 30 + 12.50x

Front

If a cell phone company charges a monthly fee plus a per-minute rate, how would you express Juanita's bill if she uses x minutes?

Back

C = 15 + 0.20x

Front

What is the slope of the equation y = 100 - 30x?

Back

The slope is -30, indicating that for each minute, the height decreases by 30 feet.

Front

How do you determine the total cost of renting a paddle boat for h hours if there is a deposit and a per-hour charge?

Back

C = 2h + 15, where C is the total cost, 2 is the hourly rate, and 15 is the deposit.

Front

What is the first step in solving a word problem involving linear equations?

Back

The first step is to read the problem carefully and identify the key information and what is being asked.

Front

What is the significance of the y-intercept in a linear equation?

Back

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