Question

Write an equation of the line that passes through the points. (2,8), (-2,10)

Answer 1

Explanation.

The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)

To do this, we can use the formula:

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

In our case, we have

`\begin{gathered} x_1=2 \\ y_1=8 \\ x_2=-2 \\ y_2=10 \end{gathered}`

We will simply put all the values above into the formula to get the equation of the line

`(10-8)/(-2-2)=(y-8)/(x-2)`

Simplifying further

`\begin{gathered} (2)/(-4)=(y-8)/(x-2) \\ \\ -(1)/(2)=(y-8)/(x-2) \end{gathered}`

Cross multiplying

`\begin{gathered} y-8=-(1)/(2)\left(x-2\right) \\ y-8=-(1)/(2)x+1 \\ y=-(1)/(2)x+1+8 \\ y=-(1)/(2)x+9 \end{gathered}`

Therefore, the equation of the line is

`y=-(1)/(2)x+9`