How Do You Find Slope with Two Points, Given Their Coordinates and That the Line Passes Through Them?
Answer – The slope of a line passing through two given points can be calculated using the formula m = (y₂ − y₁) / (x₂ − x₁).
Explanation:
To calculate the slope of a line when given two points it passes through, we use the point-slope form of the equation of a straight line:
y₂ − y₁ = m (x₂ − x₁)
Where
y₂ is the y coordinate of the second point
y₁ is the y coordinate of the first point
m is the slope of the line
x₂ is the x coordinate of the second point
x₁ is the x coordinate of the first point
The above formula can be rearranged to get the formula for the slope:
m = (y₂ − y₁) / (x₂ − x₁)
Let’s consider an example to understand this better.
Assume that a straight line passes through two points with coordinates (10, 5) and (13, 8).
While applying the formula for the slope, any one of the two points can be considered as the first point and the other as the second.
So if we consider (10, 5) as (x₁, y₁) and (13, 8) as (x₂, y₂) and substitute them in the formula for the slope, we get:
m = (8 − 5) / (13 − 10)
m = 3 / 3
m = 1
Therefore, the slope of the line passing through the given points is 1.
Popular Questions
- A Diginacci sequence is created as follows. The first two terms are any positive whole numbers. Each of the remaining terms is the sum of the digits of the previous two terms For example, starting with 4 and 8 the Diginacci sequence is 4, 8, 13, 12, 7, 10, … The calculations for this exmaple are 4 + 8 = 13, 8 + 1 + 3 = 12, 1 + 3 + 1 + 2 = 7, 1 + 2 + 7 = 10 a. Calculate the first 28 terms of the Diginacci sequence with starting terms 1 and 1, and then find the 2021st number in the sequence. b. Show that if both starting terms in a Diginacci sequence are ach less than one million, then its fourth and fifth terms are each less than 100. c. Show that if both starting terms in a Diginacci sequence are each less than 100, then it has a term after which all terms are at most 20. d. Show that if both starting terms in a Diginacci sequence are each less than 100, then it has a term after which all terms equal 18 or all terms are less than 18.
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