Answer:
[tex]y=\frac{1}{3}+\frac{13}{3}[/tex]
Step-by-step explanation:
We want to write the equation of a line that passes through (5, 6) and (-1, 4).
First, let's find our slope. We can use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's let (5, 6) be (x₁, y₁) and let's let (-1, 4) be (x₂, y₂). So, our slope is:
[tex]m=\frac{4-6}{-1-5}[/tex]
Subtract:
[tex]m=-2/-6[/tex]
Reduce:
[tex]m=1/3[/tex]
So, our slope is 1/3.
Now, we can use the point-slope form, which is:
[tex]y-y_1=m(x-x_1)[/tex]
For consistency, let's let (5, 6) be (x₁, y₁). We will also substitute 1/3 for m. So:
[tex]y-6=\frac{1}{3}(x-5)[/tex]
Distribute:
[tex]y-6=\frac{1}{3}x-\frac{5}{3}[/tex]
Add 6 to both sides:
[tex]y=\frac{1}{3}x-\frac{5}{3}+\frac{18}{3}[/tex]
Add:
[tex]y=\frac{1}{3}+\frac{13}{3}[/tex]
And we're done!
