Standard Form --> Slope-Intercept Form

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 standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What does the slope-intercept form of a linear equation represent?

Back

The slope-intercept form, y = mx + b, represents a line where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation y = -3x + 12?

Back

The slope of the line is -3.

Front

What is the y-intercept of the line represented by the equation y = 2x - 4?

Back

The y-intercept of the line is -4.

Front

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

Back

To find the y-intercept from a standard form equation (Ax + By = C), set x = 0 and solve for y.

Front

What is the process to isolate y in the equation 2x + 4y = 8?

Back

To isolate y, subtract 2x from both sides and then divide each term by 4.

Front

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

Back

The slope indicates the steepness of the line and the direction it moves; a positive slope rises, while a negative slope falls.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope.