Answer:
[tex]\sf y =\dfrac{-1}{3}x + 7[/tex]
Step-by-step explanation:
Equation of line: y =mx +b
Here, m is the slope and b is the y-intercept.
Parallel lines have same slope.
[tex]\sf y =\dfrac{-1}{3}x + 4[/tex]
So, the slope of the required line = -1/3
Equation of the required line:
[tex]\sf y =\dfrac{-1}{3}x + b[/tex]
Point(6,5) goes through the line. substitute x = 6 and y =5 in the above equation and then we can find the value of y-intercept 'b'
[tex]\sf 5 =\dfrac{-1}{3}*6 +b\\\\ 5 = -2 + b\\\\5+2 = b\\\\\boxed{b = 7}[/tex]
Equation of the require line:
[tex]\sf \boxed{\bf y =\dfrac{-1}{3}x+7}[/tex]
