Parallel and Perpendicular Lines, Equations, Through a Point

Front

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

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as 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, meaning their slopes are opposite reciprocals.

Front

If a line has a slope of 2, what is the slope of a line that is perpendicular to it?

Back

The slope of a line that is perpendicular to a line with slope 2 is -1/2.

Front

Write the equation of a line in slope-intercept form that is parallel to y = 3x + 1 and passes through the point (2, 5).

Back

y = 3x - 1.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you determine the y-intercept of a line from its equation?

Back

The y-intercept can be found by setting x = 0 in the equation and solving for y.

Front

What is the equation of a line that passes through the point (1, 2) with a slope of 4?

Back

y = 4x - 2.

Front

If a line has the equation y = -2x + 3, what is its slope?

Back

The slope of the line is -2.