# Is the slope of a horizontal line always positive?

## Is the slope of a horizontal line always positive?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

**What’s the slope of a vertical line?**

undefined slope

Vertical lines are said to have “undefined slope,” as their slope appears to be some infinitely large, undefined value. See the graphs below that show each of the four slope types.

### What is the slope of a constant horizontal line?

The slope of a horizontal line is zero while the slope of a vertical line is undefined. Slopes represent a line’s ratio of vertical change to horizontal change. Because horizontal and vertical lines remain constant and never increase or decrease, they’re merely straight lines. Horizontal lines have no steepness at all.

**Do straight lines have positive slopes?**

Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. We will learn in other sections that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.

#### Why is a horizontal line always zero?

The slope of a horizontal line is always 0. This is because the numerator in the rise over run fraction is always 0.

**What lines have the same slope?**

As mentioned above, parallel lines have the same slope.

## What does a zero slope mean?

A slope of zero means that there is a constant relationship between x and y. Graphically, the line is flat; the rise over run is zero.

**How do you tell if a slope is positive or negative?**

If the line is sloping upward from left to right, so the slope is positive (+). If the line is sloping downward from left to right, so the slope is negative (-). In our pizza example, a positive slope tells us that as the number of toppings we order (x) increases, the total cost of the pizza (y) also increases.

### How do you find a slope of a straight line?

Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: Slope =riserun Slope = rise run .

**When is the slope of a line positive or negative?**

The slope of a line is a measurement of the steepness and direction of a nonvertical line. When a line slants from lower left to upper right, the slope is a positive number. Item (a) in Figure 1 shows a line with a positive slope. When a line slants from upper left to lower right, the slope is a negative number (b).

#### Where does the slope of a non-vertical line come from?

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G8-M4-TE-1.3.0-09.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 15: The Slope of a Non-Vertical Line Classwork Opening Exercise Graph A Graph B

**Do you know the slope of a graph?**

• Students know slope is a number that describes the steepness or slant of a line. • Students interpret the unit rate as the slope of a graph. Slope is a number that describes the steepness of a line. Slope is represented by the symbol m. Lines that are left-to-right inclining have a positive slope.

## What is the slope of a decreasing line?

For the second line, y= -2x+ 3, the slope was m= -2. And the line, as you moved from left to right along the x-axis, was heading down toward the bottom of the drawing; technically, the line was “decreasing”. This relationship is always true: Increasing lines have positive slopes, and decreasing lines have negative slopes.