Answer:
[tex]y - 9 = -\frac{4}{3}(x - 3)[/tex]
Step-by-step explanation:
Given the points (3, 9) and (9, 1), we must first solve for the slope of the line before proceeding with writing the point-slope form.
In order to solve for the slope (m ), use the following formula:
m = (y₂ - y₁)/(x₂ - x₁)
Let (x₁, y₁) = (3, 9)
(x₂, y₂) = (9, 1)
Substitute these values into the given formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (1 - 9)/(9 - 3)
[tex]m = \frac{-8}{6} = \frac{-4}{3}[/tex]
Therefore, the slope of the line, m = -4/3.
Next, using the slope, m = -4/3, and one of the given points, (x₁, y₁) = (3, 9), substitute these values into the following point-slope form:
y - y₁ = m(x - x₁)
[tex]y - 9 = -\frac{4}{3}(x - 3)[/tex] ⇒ This is the point-slope form.
