Linear Equations from Tables and Graphs

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 of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

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

Back

To find the slope from a table, calculate the change in y (rise) divided by the change in x (run) between two points: slope = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear equation?

Back

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

Front

How can you write an equation from a graph?

Back

To write an equation from a graph, identify the slope and y-intercept. Use the slope-intercept form y = mx + b, substituting m for the slope and b for the y-intercept.

Front

What does the term 'rate of change' mean?

Back

The rate of change refers to how much one quantity changes in relation to another quantity. In linear equations, it is represented by the slope.

Front

How do you determine if an equation represents a linear relationship?

Back

An equation represents a linear relationship if it can be written in the form y = mx + b, where m and b are constants.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and y-intercept of the line. The coefficient of x (m) indicates the slope, while the constant term (b) indicates the y-intercept.

Front

How can you verify if an equation matches a table of values?

Back

To verify if an equation matches a table, substitute the x-values from the table into the equation and check if the resulting y-values match those in the table.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.