Answer :
Answer: The equation for the line in point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]
The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
Step-by-step explanation:
The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-
[tex](y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)[/tex]
The equation for the line in point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]
Further if we simplify the equation , we get
[tex] y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]