Writing Equations in Standard Form from Graphs

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 does the slope of a line represent in a linear equation?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

How can you determine the x-intercept from a linear equation in standard form?

Back

To find the x-intercept, set y = 0 in the equation Ax + By = C and solve for x.

Front

What is the significance of the coefficients A, B, and C in the standard form of a linear equation?

Back

A and B determine the slope of the line, while C represents the point where the line intersects the axes.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

How do you graph a linear equation in standard form?

Back

To graph a linear equation in standard form, find the x-intercept and y-intercept, plot these points, and draw a line through them.

Tags

CCSS.HSF-IF.C.7A

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.5

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other.

Tags

CCSS.8.EE.B.6

Front

How can you identify the slope from a linear equation in standard form?

Back

The slope can be found by rearranging the standard form equation into slope-intercept form (y = mx + b) and identifying the coefficient of x.

Tags

CCSS.8.EE.B.5