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 :

$\heartsuit\;Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}$

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

$\heartsuit\;Slope(m) = \frac{6 - 1}{-6 - 9} = \frac{5}{-15} = \frac{-1}{3}$

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 $m = \frac{-1}{3}$

Equation of the line :

⇒ $y - 6 = \frac{-1}{3}(x + 6)$

⇒ 3y - 18 = -x - 6

⇒ 3y = -x + 12

⇒ Slope - Intercept Form :  $y = (\frac{-1}{3})x + 4$