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Chapter 3: Problem 82

In the following exercises, find the slope of each line. $$ y=-2 $$

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

Identify the Line

The given equation is the line equation: \[ y = -2 \]
02

Identify the Form of the Equation

Recognize that the equation \( y = -2 \) is a horizontal line because it only specifies the y-coordinate and is independent of x.
03

Determine the Slope of a Horizontal Line

The slope of a horizontal line is always 0, because there is no change in y as x changes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Horizontal Line
A horizontal line is a straight line on the coordinate plane where all points have the same y-coordinate. This means, no matter how far you move left or right (along the x-axis), the y-value remains constant. In simpler terms, it stays flat. The general form of the equation for a horizontal line is: y = c , where 'c' is a constant. The line extends infinitely left and right but does not go up or down.
Slope
The slope of a line measures its steepness and is usually represented by the letter 'm'. It's calculated as the 'rise' over the 'run', which means the change in the y-coordinate divided by the change in the x-coordinate: m = (change in y)/(change in x) . However, for horizontal lines like y = -2, the 'rise' or change in y is zero because the y-coordinate remains constant. So, the slope (m) of a horizontal line is always 0. A slope of 0 indicates a flat line.
Linear Equations
Linear equations represent straight lines on a coordinate plane. They come in various forms like slope-intercept form (y = mx + b), standard form (Ax + By = C), and point-slope form (y - y1 = m(x - x1)). In the case of horizontal lines, the equation takes a simpler form: y = c , where c is a specific y-value. In today's exercise, we saw the equation y = -2, which tells us that every point on this line has a y-coordinate of -2, and the slope is 0. Understanding these forms can help you better identify and graph different lines.

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