Linear Equations from Tables

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 point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How can you determine if a set of points forms a linear relationship?

Back

A set of points forms a linear relationship if they can be connected by a straight line on a graph.

Front

What is a table of values in relation to linear equations?

Back

A table of values lists pairs of x and y coordinates that satisfy a linear equation, showing how y changes as x changes.

Front

How do you find the slope from a table of values?

Back

To find the slope from a table of values, use the formula m = (y2 - y1) / (x2 - x1) using two points (x1, y1) and (x2, y2) from the table.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that the y-value does not change as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value does not change, leading to a division by zero in the slope formula.