Equations of Lines

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 slope 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 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

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the equation of a line with a slope of 3 that passes through the point (0, -4)?

Back

The equation is y = 3x - 4.

Front

How do you convert the standard form of a line Ax + By = C to slope-intercept form?

Back

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

Front

What is the y-intercept of the line y = -2x + 5?

Back

The y-intercept is 5, which is the point (0, 5) on the graph.

Front

Find the equation of the line that is parallel to y = 4x + 1 and passes through (2, 3).

Back

The equation is y = 4x - 5.

Front

Find the equation of the line that is perpendicular to y = -1/2x + 3 and passes through (4, 2).

Back

The equation is y = 2x - 6.