Linear Equations from Tables (2)

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 the purpose of a table in relation to linear equations?

Back

A table organizes pairs of values (x, y) that can be used to identify the relationship between the variables and to plot the points on a graph.

Front

How do you find the slope using two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean if the slope of a linear equation is positive?

Back

If the slope is positive, it means that as the value of x increases, the value of y also increases, indicating a direct relationship.

Front

What does it mean if the slope of a linear equation is negative?

Back

If the slope is negative, it means that as the value of x increases, the value of y decreases, indicating an inverse relationship.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you convert a linear equation from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.