Answer:
y-4=5/4(x+6)
Step-by-step explanation:
[tex]y-y_{1} =m(x-x_{1} )[/tex] is point slope form of equation of a line.
given points are :
(-6,4) and (2,-9) where
[tex]x_{1} =-6 , y_{1} =4[/tex]
[tex]x_{2} =-2,y_{2} =9[/tex]
We have to find slope by using above points.
m= [tex]y_{2} -y_{1} /x_{2} -x_{1}[/tex]
m= 9-4 / -2-(-6)
m= 5/-2+6
m=5/4
now, take point [tex](x_{1} ,y_{1} )[/tex] and put the value of slope in point-slope form of equation:
y-4=5/4(x-(-6))
y-4=5/4(x+6) is point-slope form of equation for the line that passes through the points (-6,4) and (-2,9) .
