1 Answer

Phwd · Answer 1 · 2023-01-31T21:08:01+0000

Line equation

We know that the equation of a line is given by

y = mx + b, where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.

In order to find the equation we must find m and b.

Let's say (5, 6) is the first point and (2, -1) is the second:

(x₁, y₁) = (5, 6)

(x₂, y₂) = (2, -1)

Slope: m

Step 1

First, we the change of each variables from point 1 to point 2:

Δx = x₂ - x₁ = 2 - 5

Δx = -3

Δy = y₂ - y₁ = -1 - 6

Δy = -7

Step 2

We find the slope just by dividing each change of variable:

m = Δy/Δx = -7/-3

m= 7/3

Then, our equation should look like

y = 7/3x + b

From the equation, we can solve for b:

y = 7/3x + b

↓ subtracting 7/3x both sides

y - 7/3x = b

If we replace x and y by one of the points, we will have b:

y - 7/3x = b

↓ replacing with the first point (2, -1) = (x, y)

-1 - 7/3 · 2 = b

$\begin{gathered} b=-1-(7)/(3)\cdot2 \\ =-1-(14)/(3) \\ =-(3)/(3)-(14)/(3) \\ =-(17)/(3) \end{gathered}$

Then,

b = -17/3