Linear Equations from Tables

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How can you determine the slope from a table of values?

Back

To determine the slope from a table of values, calculate the change in y (Δy) divided by the change in x (Δx) between two points: slope (m) = (y2 - y1) / (x2 - x1).

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 do 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 involving x and y on one side and the constant on the other.

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as the value of x increases, the value of y decreases. This means the line falls from left to right.

Front

What does it mean if a linear equation has a slope of zero?

Back

If a linear equation has a slope of zero, it means the line is horizontal, indicating that the value of y remains constant regardless of the value of x.

Front

How can you identify a linear relationship from a set of data points?

Back

A linear relationship can be identified if the data points form a pattern that can be approximated by a straight line when graphed.

Front

What is the relationship between the coefficients of x and the slope in a linear equation?

Back

In the equation y = mx + b, the coefficient m represents the slope of the line. Therefore, the slope is directly determined by the coefficient of x.