step 1 Hello, so here we're told we go through the point 6 comma negative 6, but our slope is equal to

(6,-6), slope 0 | Numerade

Name: Problem 67, Chapter 3: Beginning and Intermediate Algebra
Uploaded: 2022-02-09T03:25:08-08:00
Duration: 24 s
Channel: Nick Johnson
Description: (6,-6), slope 0

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Key Concepts

Equation of a Line

The equation of a line provides a mathematical description of every point on the line in the coordinate plane. Whether using the slope-intercept form, point-slope form, or other representations, understanding how to derive and manipulate the equation is fundamental in coordinate geometry.

Point-Slope Form

The point-slope form of a linear equation is used to construct the equation of a line when a point on the line and the slope are known. It is given by the formula y - y? = m(x - x?), where (x?, y?) is a specific point on the line and m is the slope. For a horizontal line where m is 0, this form simplifies to y - y? = 0, or simply y = y?.

Slope

Slope is a measure of the steepness and direction of a line in the coordinate plane. It is calculated as the ratio of the vertical change to the horizontal change between any two points on the line. A slope of 0 indicates that there is no vertical change as one moves along the line, meaning the line is perfectly horizontal.

Horizontal Lines

A horizontal line is one that runs left to right with no upward or downward tilt, which corresponds to a slope of 0. The equation of any horizontal line is of the form y = c, where c is a constant representing the y-coordinate of every point on the line.

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