Answer: [tex]y=\dfrac{-4}{7}x+11[/tex]
Step-by-step explanation:
The slope intercept form of line with slope 'm' is given by :-
[tex]y=mx+c[/tex] , where c is the y-intercept.
The equation of a line that passes through (a,b) and having slope 'm' is
[tex](y-b)=m (x-a)[/tex]
The given point point : (4,3)
Slope : [tex]\dfrac{-4}{7}[/tex]
[tex](y-3)=\dfrac{-4}{7}(x-14)\\\\\Rightarrow\ y-3=\dfrac{-4}{7}x+\dfrac{4}{7}\times14\\\\\Rightarrow\ y-3=\dfrac{-4}{7}x+8\\\\\Rightarrow\ y=\dfrac{-4}{7}x+8+3\\\\\Rightarrow\ y=\dfrac{-4}{7}x+11[/tex]
, which is in intercept form.
Thus , the equation of the line in slope-intercept form : [tex]y=\dfrac{-4}{7}x+11[/tex]
