Question

Find the equation for the line (-1,3) and (5,-5)

Answer 1

We need to find the line equation for the line passing through (-1,3) and (5,-5).

First, we need to find the slope using the slope formula:

`m=(y_2-y_1)/(x_2-x_1_)`

Replace using P1(-1,3) and P2(5,-5).

Therefore:

`m=(-5-3)/(5-(-1))=(-8)/(6)=-(4)/(3)`

Then, we need to find the line :

`y-y_1=m(x-x_1)`

Use m= -4/3 and P1(-1,3). Then:

`\begin{gathered} y-3=-(4)/(3)(x-(-1)) \\ y-3=-(4)/(3)x-(4)/(3) \\ y=-(4)/(3)x-(4)/(3)+3 \\ y=-(4)/(3)x+(5)/(3) \end{gathered}`

Hence, the line equation is:

`y=-(4)/(3)x+(5)/(3)`