Word problems, creating linear equations, Review

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

How do you represent a situation where a quantity is increasing over time?

Back

You can represent it with a linear equation of the form y = mx + b, where m is the rate of increase and b is the initial quantity.

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).

Front

How do you write a linear equation for a situation where a quantity is decreasing?

Back

You can write it in the form y = b - mx, where b is the initial quantity and m is the rate of decrease.

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 linear relationship.

Front

How do you create a linear equation from a word problem?

Back

Identify the quantities involved, determine the rate of change, and establish the initial value to form the equation in the form y = mx + b.

Front

If a plant is 5cm tall and grows 3cm each month, what is the equation for its height after x months?

Back

y = 3x + 5.

Front

A man descends from a height of 100 feet at a rate of 30 feet per minute. Write the equation for his height after x minutes.

Back

y = 100 - 30x.

Front

If a rental service charges $8.50 per hour plus a $25.50 fee, what is the equation for total cost y in terms of hours x?

Back

y = 8.5x + 25.5.

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.