Converting Linear Equations between forms

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 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 slope-intercept form?

Back

Slope-intercept form is a way of writing linear equations in the form y = mx + b, where m is the slope and b is the y-intercept.

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 linear equation?

Back

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

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the process to rewrite an equation in standard form?

Back

To rewrite an equation in standard form, rearrange the equation to isolate the variables on one side and the constant on the other, ensuring A, B, and C are integers.

Front

What is the significance of the coefficients in standard form?

Back

In standard form Ax + By = C, A and B indicate the direction of the line, while C represents the position of the line relative to the origin.

Front

How do you convert the equation y = mx + b to standard form?

Back

To convert y = mx + b to standard form, rearrange it to the form Ax + By = C by moving mx to the left side.

Front

What is the relationship between slope and parallel lines?

Back

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