4.1 Writing Equations Given 2 Points

Front

What formula can be used to find the slope of a line?

Back

The formula to find the slope (m) of a line given two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1).

Front

What does 'm' represent in the equation of a line?

Back

In the equation of a line (y = mx + b), 'm' represents the slope of the line.

Front

What does 'b' represent in the equation of a line?

Back

In the equation of a line (y = mx + b), 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you calculate the y-intercept from two points?

Back

To calculate the y-intercept (b) from two points, first find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Then, use one of the points in the equation y = mx + b to solve for b.

Front

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

Back

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

Front

If the slope of a line is zero, what does that indicate about the line?

Back

A slope of zero indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero in the slope formula.

Front

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

Back

Two lines are parallel if they have the same slope (m).

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1).

Front

What is the general form of the equation of a line?

Back

The general form of the equation of a line is Ax + By + C = 0, where A, B, and C are constants.