Three Forms of Linear Equations

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 are the x- and y-intercepts of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is the point where the line crosses the y-axis (x=0).

Front

How do you find the slope of a line given 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 does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

How do you identify the slope and y-intercept from the equation y = mx + b?

Back

In the equation y = mx + b, m represents the slope and b represents the y-intercept.

Front

What is the relationship between parallel lines in terms of slope?

Back

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

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other; if one line has a slope of m, the other has a slope of -1/m.

Front

How can you determine if a point lies on a line given its equation?

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation and see if the resulting y-value matches the y-coordinate of the point.