The equation of a line is given. Find the slope of a line that is a. parallel to the line with t

step 1 Okay, if we have an equation of a simple y equals nine, and you have your plane and one, two, th

The equation of a line is given. Find the slope of a line...

Key Concepts

Perpendicular Lines

Perpendicular lines are lines that intersect at right angles (90 degrees). In coordinate geometry, if one line has a defined slope, the slope of a line perpendicular to it is the negative reciprocal of that slope. In the special case where one line is horizontal (slope = 0), the perpendicular line is vertical, and as vertical lines do not have a defined slope, their slope is considered undefined.

Parallel Lines

Parallel lines are lines in the same plane that never intersect; they have identical slopes. In problems involving lines, knowing that parallel lines share the same slope allows one to easily determine the equation of any line parallel to a provided line by ensuring the slope remains constant.

Horizontal Lines

Horizontal lines are lines where all points share the same y-coordinate, resulting in a slope of 0. This uniformity means that horizontal lines are completely flat, and their lack of steepness profoundly influences their relationship with other types of lines, such as determining the slopes of lines parallel or perpendicular to them.

Slope of a Line

The slope of a line is a numerical measure of its steepness, defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. A slope of 0 indicates that the line is horizontal, meaning there is no vertical change. An undefined slope, often described as infinite, is characteristic of vertical lines.

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