Question

Which of the following is a point slope equation of a line that passes through the points

Answer 1

Choice D is the answer.

Explanation:

We have given two points.

Let (x₁,y₁) = (-1,4) and (x₂,y₂) = (8,-2)

We have to find the point-slope form of the line that passes through the given points.

y-y₁ = m(x-x₁) is point-slope form of the line that passes through the points.

m is slope of line.

m = y₂-y₁ / x₂-x₁

Putting values in above formula , we have

m = -2-4 / 8-(-1)

m = -6 / 9

m = -2/3

Putting values of slope and using a point , we have

y-4 = -2/3(x-(-1))

y-4 = -2/3(x+1) is point-slope form of line that passes through the points (-1,4) and (8,-2).

Answer 2

For this case we have that the slope of a line is given by:

`m = \frac {y2-y1} {x2-x1}`

If we have the points:

`(-1,4)\\(8, -2)\\m = \frac {-2-4} {8 - (- 1)}\\m = \frac {-6} {9}\\m = - \frac {2} {3}\\`

Thus, the equation is of the form:

`y-y_ {0} = - \frac {2} {3} (x-x_ {0})`

Substituting any of the points we have:

`y-4 = - \frac {2} {3} (x - (- 1))\\y-4 = - \frac {2} {3} (x + 1)`

Answer:

Option D