Question

Find an equation for the line that passes through the points (1, -3) and (-5,5).=X$?

Answer 1

To answer this question we will use the following two-point formula for the equation of a line:

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

Therefore the equation of the line that passes through the points (1, -3) and (-5,5) is:

`y-(-3)=(5-(-3))/(-5-1)(x-1).`

Simplifying the above result we get:

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

Subtracting 3 from the above result we get:

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

Answer:

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