Respuesta :
Answer:
The Slope is
[tex]slope=m=\dfrac{-5}{4}[/tex]
The Equation is
[tex](y+1})=\dfrac{-5}{4}\times x[/tex]
Step-by-step explanation:
Two Point Form
Given:
Let,
point A( x₁ , y₁) ≡ ( 0 ,-1)
point B( x₂ , y₂ )≡ (-4 , 4)
To Find:
Equation of Line AB =?
Solution:
[tex]slope=m=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting the point A( x₁ , y₁) ≡ ( 0 ,-1) and B( x₂ , y₂ )≡ (-4 , 4) we get
[tex]slope=m=\dfrac{4--1}{-4-0}=\dfrac{5}{-4}=\dfrac{-5}{4}[/tex]
Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,
[tex](y-y_{1})=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\times (x-x_{1})[/tex]
Now on substituting the slope and point A( x₁ , y₁) ≡ ( 0 ,-1) and B( x₂ , y₂ )≡ (-4 , 4) we get
[tex](y--1})=\dfrac{4--1}{-4-0}\times (x-0)[/tex]
[tex](y+1})=\dfrac{-5}{4}\times x[/tex]
OR
Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,
i.e equation in point - slope form
[tex](y-y_{1})=m(x-x_{1})[/tex]
Substituting the values we get
[tex](y+1})=\dfrac{-5}{4}\times x[/tex]
