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 slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a service charge is a fixed amount, how is it represented in a linear equation?

Back

A fixed service charge is represented as a constant term (b) in the linear equation, added to the variable term (mx) that represents the variable cost.

Front

In the equation y = 25x + 40, what do the numbers 25 and 40 represent?

Back

In the equation y = 25x + 40, 25 represents the rate of change (slope) per hour, and 40 represents the fixed service fee.

Front

How do you determine the total cost from a linear equation?

Back

To determine the total cost from a linear equation, substitute the value of the variable (e.g., hours used) into the equation and solve for y.

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, including the variables and their relationships.

Front

What is an example of a linear equation in a real-world context?

Back

An example is the equation C = 15 + 0.20x, which represents a cell phone bill where C is the total cost, 15 is the monthly fee, and 0.20 is the cost per minute.