Question

(PICTURE) Which equation is a point slope form equation for line AB ?

y−1=3/4(x−2)

y−6=3/4(x−5)

y−2=3/4(x−1)

y−5=3/4(x−6)

Answer 1

The last one : y - 5 =
`(3)/(4)`(x - 6)

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(- 2, - 1 ) and (x₂, y₂ ) = (B(6, 5 )

m =
`(5+1)/(6+2)` =
`(6)/(8)` =
`(3)/(4)`

using (a, b ) = (6, 5 ), then

y - 5 =
`(3)/(4)`(x - 6 ) ← in point- slope form