Respuesta :
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
y- intercept: 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
[tex]\begin{gathered} b=-1-\frac{7}{3}\cdot2 \\ =-1-\frac{14}{3} \\ =-\frac{3}{3}-\frac{14}{3} \\ =-\frac{17}{3} \end{gathered}[/tex]Then,
b = -17/3
