Writing Equations from Tables

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 'solving for x' mean?

Back

It means finding the value of the variable x that makes the equation true.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does the slope (m) represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept is the value of y when x is 0, indicating where the line crosses the y-axis.

Front

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

Back

Identify the pattern in the table, determine the slope and y-intercept, and then write the equation in the form y = mx + b.

Front

If the table shows (1, 5) and (2, 9), what is the slope?

Back

The slope (m) is (9-5)/(2-1) = 4.

Front

What is the equation for the table with points (0, 3) and (1, 7)?

Back

The equation is y = 4x + 3.

Front

What does it mean if an equation has no solution?

Back

It means there is no value of the variable that can satisfy the equation, often resulting in a contradiction.

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the one that is changed or controlled, while the dependent variable is the one that is measured or affected.