4.9 Use Patterns to Write & Solve Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does the variable 'y' represent in an equation?

Back

In an equation, 'y' often represents the dependent variable, which changes in response to the value of the independent variable 'x'.

Front

What is the purpose of using patterns in equations?

Back

Using patterns helps to identify relationships between variables, allowing us to write equations that model real-world situations.

Front

How do you write an equation from a table of values?

Back

To write an equation from a table, look for a consistent pattern in the values of 'x' and 'y' and express that relationship mathematically.

Front

What does the equation b = 5a + 6 represent?

Back

This equation shows that the value of 'b' is determined by multiplying 'a' by 5 and then adding 6.

Front

How can you find the cost of multiple items using an equation?

Back

You can find the total cost by substituting the number of items into the equation that represents the cost per item plus any fixed fees.

Front

What does it mean if 'b' is 14 times 'a'?

Back

It means that for every unit increase in 'a', 'b' increases by 14 units, indicating a direct proportional relationship.

Front

What is the significance of the constant in an equation?

Back

The constant in an equation represents a fixed value that does not change, affecting the overall output of the equation.

Front

How do you solve for 'c' in the equation $6 + $2.50c = total cost?

Back

To solve for 'c', subtract 6 from the total cost and then divide by 2.50.

Front

What is the relationship between 'x' and 'y' in the equation y = x + 22?

Back

In this equation, 'y' increases by 22 units for every unit increase in 'x', indicating a linear relationship.