A.2C - Linear Equations from Various Forms

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 y with respect to x. It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept (b) in a linear equation?

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Front

What is the formula for the perimeter of a regular polygon?

Back

The perimeter (P) of a regular polygon can be calculated using the formula P = ns, where n is the number of sides and s is the length of one side.

Tags

CCSS.3.MD.D.8

Front

How can you determine the equation of a line from a table of values?

Back

To determine the equation of a line from a table, identify the slope (change in y/change in x) and the y-intercept (value of y when x=0) from the data.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the relationship between the coefficients in the equation y = mx + b?

Back

In the equation y = mx + b, m is the slope and b is the y-intercept. The coefficients determine the steepness and position of the line on the graph.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

Front

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

Back

A negative slope indicates that as x increases, y decreases. The line falls from left to right.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5