Question

Look at the coordinates below and write a linear equation (1,2) and (5,10)

Answer 1

The coordinates are given below as

`\begin{gathered} \left(1,2\right)\Rightarrow\left(x_1,y_1\right) \\ \left(5,10\right)\Rightarrow\left(x_2,y_2\right) \end{gathered}`

Concept:

To calcute the equation of a line, we will use the formula below

`(y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1)`

By substituting the values, we will have

`\begin{gathered} (y_(2)-y_(1))/(x_(2)-x_(1))=(y-y_(1))/(x-x_(1)) \\ (10-2)/(5-1)=(y-2)/(x-1) \end{gathered}`

Cross multiply the equation above, we will have

`\begin{gathered} (10-2)/(5-1)=(y-2)/(x-1) \\ (8)/(4)=(y-2)/(x-1) \\ (2)/(1)=(y-2)/(x-1) \\ y-2=2\left(x-1\right) \\ y-2=2x-2 \\ y=2x-2+2 \\ y=2x \end{gathered}`

Hence,

The equation of the line is y=2x