A.2BCEFGH Equations & Inequalities DA#3 REDO

Front

What is a linear function?

Back

A linear function is a mathematical function that creates a straight line when graphed. It can be expressed 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 function represent?

Back

The slope represents the rate of change of the function. It indicates how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

What is the y-intercept in a linear function?

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 function for a real-world scenario?

Back

Identify the variables, determine the relationship between them, and express it in the form c = mt + b, where c is the total cost, m is the cost per item, t is the number of items, and b is any fixed cost.

Front

What is the total cost function for purchasing t cartridges at $18.99 each with a $7.95 shipping fee?

Back

c = 18.99t + 7.95.

Front

What does the term 'fixed cost' mean in a cost function?

Back

A fixed cost is a cost that does not change with the level of output or sales. In the context of the flashcard example, the shipping fee is a fixed cost.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What does it mean to graph a linear equation?

Back

Graphing a linear equation involves plotting points that satisfy the equation on a coordinate plane and connecting them to form a straight line.