Question

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

$\left(3,5\right),\left(5,6\right)$

Short answer

The required equation is represented by$y=\frac{1}{2}x+\frac{7}{2}$.

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)$.

$$\begin{gathered} y-5=\frac{6-5}{5-3}\left(x-3\right) \\ y-5=\frac{1}{2}\left(x-3\right) \\ y=\frac{1}{2}x-\frac{3}{2}+5 \\ y=\frac{1}{2}x+\frac{7}{2} \end{gathered}$$

Step 3. Write the conclusion.

The obtained equation is$y=\frac{1}{2}x+\frac{7}{2}$ so it is the required equation.