Question

What is the point slope form of the points?

(-4,-1) and (1 1/2, 2)

y+1=6/11(x+4)
y+1=6/7(x+4)
y+4=11/6(x+1)
y-1=6/11(x-4)

Answer 1

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 ) = (- 4, - 1) and (x₂, y₂) = (1 1/2, 2 )

m =
`(2+1)/(11/2+4)` =
`(3)/(5 1/2)` =
`(6)/(11)`

using (a, b) = (- 4, - 1), then

y + 1 =
`(6)/(11)`(x + 4)