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 the 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?

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation Ax + By = C.

Front

How do you find the x-intercept from a standard form equation?

Back

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

Front

How do you find the y-intercept from a standard form equation?

Back

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

Front

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

Back

A, B, and C determine the position and orientation of the line in the coordinate plane.

Front

What is the relationship between the slope and the coefficients in standard form?

Back

The slope (m) can be found using the formula m = -A/B from the standard form Ax + By = C.

Front

What does it mean for an equation to be in standard form?

Back

An equation is in standard form if it is written as Ax + By = C, with A, B, and C as integers and A non-negative.