4.6 Practice

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when it is 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 it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the purpose of using variables in equations?

Back

Variables are used in equations to represent unknown values that can change or vary.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the equation for a cost problem involving a fixed charge and a variable charge?

Back

The equation is typically in the form: Fixed Charge + (Variable Charge per item * Number of items) = Total Cost.

Front

If a printer charges $800 plus $5 per book, how would you express the total cost for x books?

Back

The total cost can be expressed as: 800 + 5x.

Front

What is the first step in solving the equation 800 + 5x = 4000?

Back

The first step is to subtract 800 from both sides of the equation.

Front

How do you interpret the solution of an equation in a real-world context?

Back

The solution of an equation represents the value of the variable that satisfies the conditions of the problem, often relating to quantities or measurements.

Front

What does it mean if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same relationship.

Front

In the equation 2w + 3 = 75, what does w represent?

Back

In this equation, w represents the width of the rectangular field.