Answer :
Answer:
[tex]y = \frac{1}{3}x+\frac{1}{3}[/tex]
Step-by-step explanation:
First, we need to figure out a linear equation. When given two points - [tex](x_{1}, y_{1})[/tex]and [tex](x_{2}, y_{2})[/tex] - first subtract [tex]y_{1}[/tex] from [tex]y_{2}[/tex] and and [tex]x_{1}[/tex] from [tex]x_{2}[/tex]. So in your situation, it will be [tex]2-1[/tex] and [tex]5-2[/tex]. That equals [tex]1[/tex] and [tex]3[/tex], so your slope (how much the line moves up/down per unit) will be [tex]\frac{1}{3} x[/tex].
Next, we need to find the y-intercept. To solve using point-slope form, we will plug our numbers in:
[tex]y-y_{1} = m(x-x_{1})\\y-1=\frac{1}{3}(x-2)\\y-1=\frac{1}{3}x-\frac{2}{3}\\/+1=//+1\\y = \frac{1}{3}x+\frac{1}{3}[/tex]
So our final equation is [tex]y = \frac{1}{3}x+\frac{1}{3}[/tex], which passes through both [tex](2,1)[/tex] and [tex](5,2)[/tex]. Hope this helps :)