Question

what is an equation of the line that passes through the points (4,6) and (8,7)

Answer 1

Solution

- The formula for finding the equation of a line is:

$\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ where, \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the points on the line} \end{gathered}$

- Thus, we can find the line as follows

$\begin{gathered} (x_1,y_1)=(4,6) \\ (x_2,y_2)=(8,7) \\ \\ \frac{7-6}{8-4}=\frac{y-6}{x-4} \\ \\ \frac{1}{4}=\frac{y-6}{x-4} \\ \\ \text{ Cross Multiply,} \\ \frac{1}{4}(x-4)=y-6 \\ \\ Add\text{ 6 to both sides} \\ \\ y=\frac{1}{4}(x-4)+6 \\ \\ y=\frac{1}{4}x-\frac{4}{4}+6 \\ \\ y=\frac{x}{4}+5 \end{gathered}$

Final Answer

The answer is

$y=\frac{x}{4}+5$