Question

What is an equation of the line (-3,2) and (-6,7)

Answer 1

Answer: y=-(5/3)x-3

Explanation:

`(-3,2)\ \ \ \ (-6,7)`

Аn equation of the line

`\displaystyle\\\boxed {(x-x_1)/(x_2-x_2) =(y-y_1)/(y_2-y_1) }`

`x_1=-3\ \ \ \ x_2=-6\ \ \ \ y_1=2\ \ \ \ y_2=7`

Hence,

`\displaystyle\\(x-(-3))/(-6-(-3)) =(y-2)/(7-2)\\\\(x+3)/(-6+3)=(y-2)/(5) \\\\(x+3)/(-3) =(y-2)/(5)`

Multiply both parts of the equation by 5:

`\displaystyle\\5((-x-3)/(3) )=5((y-2)/(5)) \\\\(5)/(3) (-x-3)=y-2\\\\-(5)/(3)x-(5(3))/(3) =y-2\\\\-(5)/(3) x-5=y-2\\\\-(5)/(3) x-5+2=y-2+2\\\\(5)/(3)x-3=y\\\\Thus,\ y=-(5)/(3)x-3`