Creating Linear Equations

Front

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

Back

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

Front

How do you determine the slope in a real-world scenario involving costs?

Back

The slope represents the rate of change in cost per unit, such as dollars per hour or dollars per item.

Front

What does the y-intercept represent in a cost equation?

Back

The y-intercept represents the fixed cost or initial fee before any additional charges are applied.

Front

How can you write an equation for a situation with a fixed fee and a variable cost?

Back

The equation can be written in the form y = mx + b, where m is the variable cost per unit and b is the fixed fee.

Front

What is the significance of the inequality in budgeting scenarios?

Back

Inequalities represent constraints, such as a budget limit, indicating that the total cost must not exceed a certain amount.

Front

How do you convert a word problem into a linear equation?

Back

Identify the fixed costs, variable costs, and the relationship between the variables to formulate the equation.

Front

What is the formula to calculate total cost when given a fixed fee and a variable rate?

Back

Total Cost = Fixed Fee + (Variable Rate * Number of Units) or hours.

Front

How do you interpret the solution to a linear equation in a real-world context?

Back

The solution represents the specific value of the variable that satisfies the equation, such as the number of hours until a certain cost is reached.

Front

What is the role of variables in linear equations?

Back

Variables represent quantities that can change, such as time, number of items, or hours rented.

Front

How do you graph a linear equation in slope-intercept form?

Back

Start at the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to plot additional points.