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 table of values represents a linear relationship?

Back

A table of values represents a linear relationship if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the formula to find the slope between two points (x1, y1) and (x2, y2)?

Back

The formula to find the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

If a linear equation is given in the form y = mx + b, what does 'm' indicate about the line?

Back

'm' indicates the slope of the line, showing how much y changes for a unit change in x.

Front

What is the significance of a slope of 0 in a linear equation?

Back

A slope of 0 indicates a horizontal line, meaning that the value of y remains constant regardless of x.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How can you graph a linear equation using a table of values?

Back

To graph a linear equation using a table of values, calculate y for several x values, plot the points (x, y) on a coordinate plane, and draw a straight line through the points.

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.