Linear Equations Word Problem Review

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you write a linear equation from a word problem involving a startup cost and a variable cost per item?

Back

Identify the fixed startup cost and the variable cost per item. The equation can be written as y = mx + b, where m is the variable cost and b is the startup cost.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do you find the total cost in a linear equation involving hourly rates?

Back

Multiply the hourly rate by the number of hours worked and add any fixed fees to find the total cost.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

How can you determine the cost of an item if you know the total revenue and the price of another item?

Back

Set up a linear equation based on the total revenue and the known price of the other item, then solve for the unknown price.

Front

What is a one-time fee in a linear equation context?

Back

A one-time fee is a fixed cost that does not change with the number of items or hours, often represented as the y-intercept in a linear equation.

Front

How do you solve a linear equation to find an unknown fee?

Back

Isolate the variable on one side of the equation by performing inverse operations to find the unknown fee.

Front

What is the relationship between the coefficients in a linear equation and the graph of the equation?

Back

The coefficients determine the slope and y-intercept of the line, affecting its steepness and where it crosses the y-axis.

Front

How do you interpret the y-intercept in a real-world scenario?

Back

The y-intercept represents the initial value or fixed cost before any variable costs are added.