Writing Linear Equations and Inequalties

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 (m) represent in a linear equation?

Back

The slope (m) 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 (b) in a linear equation?

Back

The y-intercept (b) 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 for a situation involving a fixed salary and variable earnings?

Back

You can write the equation as S = fixed salary + (variable rate * variable amount). For example, S = 3h + 0.90d for Margaret's salary.

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, or not equal to the other.

Front

How do you represent a budget constraint in an inequality?

Back

You can represent a budget constraint by using an inequality that shows the total cost must be less than or equal to the budget. For example, 1.50x + 10 ≤ 40.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

Front

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

Back

Identify the variables, determine the fixed and variable components, and then express the relationship mathematically. For example, for tips and hourly wage, use S = 3h + 0.90d.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By ≤ C or Ax + By < C, where A, B, and C are constants.