Question

What is an equation of the line that passes through the points (8,-4) and (6,-5)?Put your answer in fully reduced form.

Answer 1

The expression for the equation of the line with the given two coordinates

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

Given pair of coordinates : (8,-4) & (6,-5)

Substitute the value and simplify

`\begin{gathered} y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1) \\ \text{Substitute x}_1=8,x_2=6,y_1=(-4),y_2=(-5) \\ y-(-4)=(-5-(-4))/(6-8)(x-8) \\ y+4=(-5+4)/(-2)(x-8) \\ y+4=(1)/(2)(x-8) \\ y=(x)/(2)-(8)/(2)-4 \\ y=(x)/(2)-4-4 \\ y=(x)/(2)-8 \\ 2y=x-16 \\ x-2y-16=0 \end{gathered}`

Answer : Equation of line is : x-2y-16=0