Answer:
[tex]y=\frac{1}{6}x+\frac{2}{3}[/tex]
Step-by-step explanation:
(8,2) (2,1)
First, you will need to find the gradient (or the m value in [tex]y=mx+b[/tex])
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
y2=1
y1=2
x2=2
x1=8
Now we can plug in these values to get the m value.
[tex]m=\frac{1-2}{2-8}[/tex]
Because the numerator and the denoinator will be negative, we needed to divide them to get a positive fraction.
[tex]m=\frac{-1}{-6} \\m=\frac{1}{6}[/tex]
Now we need to find the line of the equation using the following equation:
[tex]y-y1=m(x-x1)[/tex]
Now plug in the values using x1 and y1.
[tex]y-2=\frac{1}{6} (x-8)[/tex]
We can use the distributive property to distribute the [tex]\frac{1}{6}[/tex].
[tex]y-2=\frac{1}{6}x-\frac{4}{3}[/tex]
Lastly, we can add 2 to both sides to cancel out the -2 on the left to give us our equation.
[tex]y=\frac{1}{6}x+\frac{2}{3}[/tex]
