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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.HSF-LE.A.1B

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).

Tags

CCSS.8.EE.B.5

Front

If a linear equation has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, the value of y increases by 2 units.

Tags

CCSS.8.EE.B.5

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 the value of x.

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, resulting in a downward sloping line.

Tags

CCSS.8.EE.B.5

Front

How can you convert a table of values into a linear equation?

Back

To convert a table of values into a linear equation, first find the slope using two points, then use one of the points to solve for the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.