Question

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

$\left(2,-1\right),\left(5,2\right)$

Short answer

The required equation is represented by$y=x-3$.

Step-by-step solution

Step 1. Determine the formula that can be used.

The standard form associated with line that is having a travel through points which are two in count$y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ can be used to calculate the required equation.

Step 2. Take the help of the obtained method.

Take the help of obtained standard form represented by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$in which the required values can be filled by using the provided points as they are in the form of $\left(x_1,y_1\right)$$\left(x_2,y_2\right)$.

$$\begin{gathered} y-\left(-1\right)=\frac{2-\left(-1\right)}{5-2}\left(x-2\right) \\ y+1=\frac{3}{3}\left(x-2\right) \\ y=x-2-1 \\ y=x-3 \end{gathered}$$

Step 3. Write the conclusion.

The obtained equation is$y=x-3$ so it is the required equation.