Question

What is the equation in point slope form of the line passing through (-2,-5) and (2,3)

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 ) = (- 2, - 5 ) and (x₂, y₂ ) = (2, 3 )

m = $\frac{3+5}{2+2}$ = $\frac{8}{4}$ = 2

use either of the 2 points for (a, b)

using (a, b) = (2, 3), then

y - 3 = 2(x - 2) ← in point-slope form

Answer 2

what is the equation in point slope form of the line passing through (-2,-5) and (2,3)

Point slope form: y - y1 = m(x - x1)

m = (3 + 5)/(2 + 2) = 8/4 = 2

Point slope form:

y - 3 = 2(x - 2) if you're using this (2,3)

or

y + 5 = 2(x + 2) if you're using this (-2,-5)