Question

Find the equation of the line passing through the points (-2,14) and (1,8). Write your answer in the form y=mx+b.y=mx+b.

Answer 1

We have two-point and we need to find the equation of the line that passes through these points, for this, we use the equation of the line passing through two given points.

The equation is the following:

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

Where in this case:

`\begin{gathered} (x_1,y_1)=(-2,14) \\ (x_2,y_2)=(1,8) \end{gathered}`

Now we replace and solve "y" as follows:

`\begin{gathered} y-14=(8-14)/(1-(-2))(x-(-2) \\ y-14=(8-14)/(1+2)(x+2) \\ y-14=(-6)/(3)(x+2) \\ y-14=-2(x+2) \\ y-14=-2x-4 \\ y=-2x-4+14 \\ y=-2x+10 \end{gathered}`

In conclusion, the answer is:

`y=-2x+10`

Where:

`\begin{gathered} m=-2 \\ b=10 \end{gathered}`