Question

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

Answer 1

Given:

Given line passes through (-1,3) and (5, -5).

Required: Equation of the line

Step-by-step explanation:

First, find the slope using the two point formula.

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ =(-5-3)/(5-(-1)) \\ =(-8)/(6)=-(4)/(3) \end{gathered}`

An equation of a line in slope-intercept form is y = mx+c, where m is the slope and c is the y-intercept.

Substitute the value of m into y = mx+c.

`y=-(4)/(3)x+c...(1)`

Plug the value (-1,3) into equation (1) to find c.

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

Substitute the obtained value of c into equation (1).

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

Final Answer:

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