Question

What is the​ slope-intercept form of the equation of the​ line? (-6,6) , (9,1) PLZZZZ help me on this

Answer 1

Heya! Alexis

Line is Passing through the Points (-6 , 6) and (9 , 1)

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

`\heartsuit\;Slope(m) = (y_1 - y_2)/(x_1 - x_2)`

here x₁ = -6 and x₂ = 9 and y₁ = 6 and y₂ = 1

`\heartsuit\;Slope(m) = (6 - 1)/(-6 - 9) = (5)/(-15) = (-1)/(3)`

We know that the form of line passing through point (x₀ , y₀) and having slope m is : y - y₀ = m(x - x₀)

Here the line passes through the point (-6 , 6) and (9 , 1)

We can take any one point of the both

let us take (-6 , 6)

x₀ = -6 and y₀ = 6 and we found
`m = (-1)/(3)`

Equation of the line :

⇒
`y - 6 = (-1)/(3)(x + 6)`

⇒ 3y - 18 = -x - 6

⇒ 3y = -x + 12

⇒ Slope - Intercept Form :
`y = ((-1)/(3))x + 4`