Standard Form to 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 an 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 is slope-intercept form?

Back

Slope-intercept form is a way of expressing a linear equation as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope represent in a linear equation?

Back

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

Front

How do you find the slope from a standard form equation?

Back

To find the slope from a standard form equation (Ax + By = C), rearrange it to slope-intercept form (y = mx + b) and identify m.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in slope-intercept form.

Front

How can you calculate the y-intercept from a standard form equation?

Back

To calculate the y-intercept from a standard form equation (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 of a linear equation?

Back

A determines the steepness and direction of the line, B determines the vertical position, and C is the constant that shifts the line.

Front

What is the relationship between the slope and the direction of a line?

Back

A positive slope indicates the line rises from left to right, while a negative slope indicates it falls from left to right.

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).