Question

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

Answer 1

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

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

Final Answer

The answer is

`y=(x)/(4)+5`