The slope of a line is a measure of its steepness, and it is defined as the ratio of the change in the vertical coordinate (y) to the change in the horizontal coordinate (x) between two points on the line. In other words, it tells us how much the line rises or falls for every unit of horizontal distance.
How do you find the slope of a line?
To find the slope of a line, you need two points on the line. Let’s call these points (x1, y1) and (x2, y2). The slope of the line can be calculated using the following formula:
slope = (y2 – y1) / (x2 – x1)
This formula works for any two points on a line, regardless of their position on the line. Once you have calculated the slope, you can use it to determine other properties of the line, such as its y-intercept or equation.
Here is an example problem to demonstrate how to find the slope of a line:
Slope Of A Line Example
Find the slope of the line that passes through the points (2, 4) and (5, 9).
Step 1: Identify the values of x1, y1, x2, and y2.
In this problem, x1 = 2, y1 = 4, x2 = 5, and y2 = 9.
Step 2: Substitute these values into the formula for slope.
slope = (y2 – y1) / (x2 – x1) slope = (9 – 4) / (5 – 2) slope = 5 / 3
Therefore, the slope of the line that passes through the points (2, 4) and (5, 9) is 5/3.
It is important to note that the slope of a line can also be written as a decimal or a percentage. In the example above, the slope of 5/3 can be written as a decimal by dividing 5 by 3:
5 / 3 = 1.67 (rounded to two decimal places)
Similarly, the slope can be written as a percentage by multiplying the decimal form by 100:
1.67 × 100 = 167%
It is also worth mentioning that the slope of a vertical line is undefined, while the slope of a horizontal line is 0. This is because a vertical line has an infinite slope, while a horizontal line has no rise and therefore no slope.
In summary, finding the slope of a line involves identifying two points on the line, calculating the difference in their y-coordinates and x-coordinates, and then dividing the former by the latter. This ratio represents the steepness of the line and can be expressed as a fraction, decimal, or percentage.