Solving Equations

Front

What is an explicit equation?

Back

An explicit equation is a mathematical expression that defines a relationship between variables, allowing you to calculate the output directly from the input.

Front

How do you identify the pattern in a sequence?

Back

To identify the pattern in a sequence, look for a consistent difference between consecutive terms, which can help you derive the explicit equation.

Front

Given the sequence: 25, 21, 17, 13,... what is the common difference?

Back

The common difference is -4, as each term decreases by 4.

Front

What is the explicit equation for the sequence 25, 21, 17, 13,...?

Back

a_n = -4n + 29.

Front

How do you derive an explicit equation from a table of values?

Back

To derive an explicit equation from a table, identify the relationship between the x-values and y-values, often using slope-intercept form (y = mx + b).

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the y-intercept in the equation f(x) = 4x + 3?

Back

The y-intercept is 3, which is the value of f(x) when x = 0.

Front

Given the table of values, how do you find the explicit equation?

Back

Use two points from the table to calculate the slope (m) and then use one point to find the y-intercept (b) to form the equation y = mx + b.

Front

What is the explicit equation for the table that results in f(x) = 4x + 3?

Back

The explicit equation is f(x) = 4x + 3.

Front

What is the explicit equation for the table that results in f(x) = 3x - 9?

Back

The explicit equation is f(x) = 3x - 9.