Question

What is the equation of the line that is parallel to the line y = -1/3x+4 and passes through the point (6,5)

Answer 1

Answer:

$\sf y =\dfrac{-1}{3}x + 7$

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.

            $\sf y =\dfrac{-1}{3}x + 4$

     So, the slope of the required line = -1/3

Equation of the required line:  

                $\sf y =\dfrac{-1}{3}x + b$

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'

    $\sf 5 =\dfrac{-1}{3}*6 +b\\\\ 5 = -2 + b\\\\5+2 = b\\\\\boxed{b = 7}$

Equation of the require line:

           $\sf \boxed{\bf y =\dfrac{-1}{3}x+7}$