Writing equations from two points

Front

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

Back

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

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 does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

Given two points (x1, y1) and (x2, y2), how can you find the equation of the line that passes through them?

Back

1. Calculate the slope (m) using m = (y2 - y1) / (x2 - x1). 2. Use one of the points to solve for b in the equation 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 can you determine if two lines are parallel using their equations?

Back

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

Front

What is the formula for converting the standard form of a linear equation Ax + By = C to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other; if one slope is m, the other is -1/m.

Front

How do you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.

Front

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

Back

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