Question

Complete the point-slope equation of the line through (-1, 6) and (1, 5). Use exact numbers. y - 6 =

Answer 1

We need the two points to find the slope:

slope = y2 - y1 / x2 - x1

slope = 5 - 6 / 1 - (-1)

slope = -1 / 1 + 1

slope = -1 / 2

m = -1/2

Now, I use that for the point slope equation : y - y1 = m(x - x1).

Just stick in the values.

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

y - 6 = -1/2(x + 1)

↑ Complete Point - Slope equation

Answer 2

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

Explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 1, 6 ) and (x₂, y₂ ) = (1, 5 )

m =
`(5-6)/(1-(-1))` =
`(-1)/(1+1)` = -
`(1)/(2)`

using (a, b ) = (- 1, 6 ) , then

y - 6 = -
`(1)/(2)` (x - (- 1) ) , that is

y - 6 = -
`(1)/(2)` (x + 1) ← equation of line in point- slope form