Question

the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).

Answer 1

`\large\boxed{for\ (-3,\ 2):\ y-2=-(1)/(5)(x+3)}\\\boxed{for\ (2,\ 1):\ y-1=-(1)/(5)(x-2)}`

Explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

========================================

We have the points (-3, 2) and (2, 1).

Substitute:

`m=(1-2)/(2-(-3))=(-1)/(5)=-(1)/(5)`

for (-3, 2)

`y-2=-(1)/(5)(x-(-3))\\\\y-2=-(1)/(5)(x+3)`

for (2, 1)

`y-1=-(1)/(5)(x-2)`