Linear Equation 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 of a line 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 an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and translate the words into a mathematical equation.

Front

What does the equation y = 8x + 42.5 represent in a word problem?

Back

It represents a situation where a total amount y is calculated based on a fixed cost of $42.50 and a variable cost of $8.00 for each unit x.

Front

How do you find the total cost in a rental situation?

Back

Total cost can be found by adding a fixed fee to a variable cost that depends on the number of hours or units used.

Front

What is the formula for total cost (C) in a rental problem with a fixed fee and a variable rate?

Back

C = fixed fee + (variable rate * number of units or hours).

Front

What is the relationship between the rate of change and slope?

Back

The rate of change is another term for slope; it describes how much y changes for a change in x.

Front

How can you determine the total pages read over time?

Back

Use the equation y = rate of reading * time + initial pages, where y is total pages read.

Front

What does the equation 73 - 2x = y represent?

Back

It represents a situation where the temperature starts at 73°F and decreases by 2°F for each hour x.