Question

Which equation is a point slope form equation for line AB?

y+1=−2(x−6)

y+2=−2(x−5)

y+6=−2(x−1)

y+5=−2(x−2)

Answer 1

Option 2: y+2=−2(x−5) is the correct answer.

Explanation:

We can see two points on the line A and B.

Their coordinates are:

A = (x1,y1) = (1,6)

B = (x2,y2) = (5,-2)

The point slope form is given as:

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

Here m is the slope which is found using the formula

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

Putting the values

`m = (-2-6)/(5-1)\\m=(-8)/(4)\\m = -2`

Putting the value of slope

`y-y1 = -2(x-x_1)`

Putting both points to get two forms of point slope form of equation

Putting (1,6):

`y-6 = -2(x-1)`

Putting (5,-2):

`y+2 = -2(x-5)`

Looking at the equations and options it can be concluded that

Option 2: y+2=−2(x−5) is the correct answer