Answer:
Therefore the equation of the line through ( 3, -8 ) and ( 7, -2) is
[tex]y=\dfrac{3}{2}x-\dfrac{25}{2}[/tex]
Step-by-step explanation:
Given
point A( x₁ , y₁) ≡ ( 3 ,-8)
point B( x₂ , y₂) ≡ (7 , -2)
To Find:
Equation of Line AB =?
Solution:
Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula
[tex](y - y_{1} )=(\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\[/tex]
Substituting the given values in a above equation we get
[tex]y-(-8)=\dfrac{-2-(-8)}{7-3}\times (x-3)\\\\y+8=\dfrac{3}{2}(x-3)\\\\2(y+8)=3(x-3)\\\\2y+16=3x-9\\y=\dfrac{3}{2}x-\dfrac{25}{2}[/tex]
Which is in Point-Slope Form i,e
[tex]y =mx +c[/tex]
Where m = slope , and c = y - intercept
Therefore the equation of the line through ( 3, -8 ) and ( 7, -2) is
[tex]y=\dfrac{3}{2}x-\dfrac{25}{2}[/tex]
