3-17 B Linear Equations

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What does the slope of a line 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

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

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is a horizontal line in terms of a linear equation?

Back

A horizontal line has a slope of 0 and can be represented by the equation y = k, where k is a constant.

Front

What is a vertical line in terms of a linear equation?

Back

A vertical line has an undefined slope and can be represented by the equation x = k, where k is a constant.

Front

How do you determine the slope from two points on a line?

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 it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the significance of the point (0, b) in the slope-intercept form?

Back

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