Equation of a line given two points

Front

What is the Point-Slope form of a line?

Back

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

Front

How do you calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the Slope-Intercept form of a line?

Back

The Slope-Intercept form of a line is given by the equation: y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept (b) of a line given its slope and a point?

Back

You can find the y-intercept (b) by rearranging the Slope-Intercept form: b = y - mx, using the slope (m) and the coordinates of the point (x, y).

Front

What is the equation of a line that passes through the points (1, 2) and (3, 4)?

Back

First, calculate the slope: m = (4 - 2) / (3 - 1) = 1. Then use the Point-Slope form: y - 2 = 1(x - 1) or y = x + 1.

Front

What is the formula for the equation of a line given two points?

Back

The formula is: y - y1 = m(x - x1), where m is the slope calculated from the two points.

Front

How do you convert from Point-Slope form to Slope-Intercept form?

Back

To convert, rearrange the Point-Slope form equation to isolate y: y = mx + 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

How do you determine if two lines are parallel?

Back

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

Front

How do you determine if two lines are perpendicular?

Back

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