Answer:
[tex]y=5-\frac{2}{3}(x-9)[/tex]
Step-by-step explanation:
We are given that the line passes through the two points (9, 5) and (6, 7).
And we want to find the equation of the line in point-slope form:
[tex]y=y_0=m(x-x_0)[/tex]
First, let's find the slope. The slope is given by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's let (9, 5) be (x₁, y₁) and let (6, 7) be (x₂, y₂). Substitute these values into the slope formula:
[tex]m=\frac{7-5}{6-9}[/tex]
Subtract:
[tex]m=2/-3[/tex]
Simplify:
[tex]m=-2/3[/tex]
So, our slope is -2/3.
Note, we can use the point-slope form. Notice that we also need an (x₀, y₀).
We can use either of our two known points. So, let's let (9, 5) be (x₀, y₀).
Substitute 9 for x₀, 5 for y₀, and -2/3 for m yields:
[tex]y=5-\frac{2}{3}(x-9)[/tex]
And we're done!
