Question

What is an equation in point-slope form of the line that passes through the point (1,−5) and (−5,−6)

HELPPPP

Answer 1

y + 5 = ¹/₆(x - 1)

Explanation:

The slope of a line passing through two given points:
`m=(y_2-y_1)/(x_2-x_1)`

(1, -5) ⇒ x₁ = 1 , y₁ = -5

(-5, -6) ⇒ x₂ = -5 , y₂ = -6

`m=(-6+5)/(-5-1)=(-1)/(-6)=\frac16`

Point-slope form of equation of a line with givem slope m and passing through point (x₁, y₁):
`y-y_1=m(x-x_1)`

(1, -5) ⇒ x₁ = 1 , y₁ = -5

Therefore:

`y-(-5)=\frac16(x-1)\\\\\underline{y+5=\frac16(x-1)}`