Lines from Two Points (Point Slope Form)

Question

Write the equation of the line that passes through the points (-1,3)(−1,3) and (-9,5)(−9,5). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

Hi Leslie!

Question is to put your answer in Point

Slope Form, which is....

y - y₁ = m (x - x₁)

where (x_1,y₁) is a point on the line

and m is the slope of the line.

We can use either (-1,3) or (-9,5)

for (x₁,y₁). I'll use (-1,3).

The other point (x₂,y₂) = (-9,5)

First we need to find the slope, m.

x₁= -1, y₁= 3, x₂=-9, y₂=5

y₂ - y₁

m = --------

x₂- x₁

5 - 3

m= ------

-9 - -1

2

m = ------

-9 + 1

2

m = ------

-8

1

m = - ---

4

substitute in for m, x₁ and y₁

y - y₁ = m (x - x₁)

1

y - 3 = - -- (x - -1)

4

1

y - 3 = - ---- (x+1)

4

Answer 2

Hi Leslie

Since you aren given two points, (-1,3) and (-9,5), you can calculate the slope, m for your line then use one of the points put in point slope form

Let the coordinates of your first point be (-1,3)

The coordinates of yours second point be (-9,5)

m = (y₂ - y₁)/(x₂ - x₁)

m = (5 - 3)/(-9-(-1))

m= 2/-8 = -1/4

Point Slope Form

y - y₁ = m(x - x₁)

Can your continue from here?