Question

. Write an equation of the line that passes through the given points use point

Answer 1

Answer:

$y = \frac{1}{3}x+\frac{1}{3}$

Step-by-step explanation:

First, we need to figure out a linear equation. When given two points - $(x_{1}, y_{1})$and $(x_{2}, y_{2})$ - first subtract $y_{1}$ from $y_{2}$ and and $x_{1}$ from $x_{2}$. So in your situation, it will be $2-1$ and $5-2$. That equals $1$ and $3$, so your slope (how much the line moves up/down per unit) will be $\frac{1}{3} x$.

Next, we need to find the y-intercept. To solve using point-slope form, we will plug our numbers in:

$y-y_{1} = m(x-x_{1})\\y-1=\frac{1}{3}(x-2)\\y-1=\frac{1}{3}x-\frac{2}{3}\\/+1=//+1\\y = \frac{1}{3}x+\frac{1}{3}$

So our final equation is $y = \frac{1}{3}x+\frac{1}{3}$, which passes through both $(2,1)$ and $(5,2)$. Hope this helps :)