Writing Linear Equations from 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 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). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

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

Front

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

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

What is the equation for total cost when there is a fixed fee and a variable cost?

Back

The equation is y = mx + b, where y is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Front

In the equation y = 15x + 40, what do the numbers 15 and 40 represent?

Back

In this equation, 15 represents the hourly rate charged, and 40 represents the fixed service fee.

Front

How do you determine the total cost from a rental problem?

Back

Add the fixed cost to the product of the variable cost per unit and the number of units used.

Front

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

Back

Read the problem carefully to identify the key information and what is being asked.

Front

What does the equation 222.5 = 35 + 0.75m represent?

Back

This equation represents the total rental charge of $222.50, where $35 is the fixed cost and $0.75 is the cost per mile driven (m).

Front

How can you express the relationship between two quantities in a word problem?

Back

You can express the relationship using an equation that combines the quantities, often in the form of Ax + By = C.