Question

Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.

Answer 1

Answer:

Step-by-step explanation:

Equation of the line in slope- intercept form:

       $\sf \boxed{\bf y = mx +b}$

Here, m is the slope and b is the y-intercept

  Find the slope with the given two points.

   $\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}$

             $\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}$

Slope = -2/3 and choose any one the given points.

Substitute m = -2/3  and (5,6)  in the above equation and find 'b'

      $\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}$

Equation of the line:

            $y = \dfrac{-2}{3}x + \dfrac{28}{3}$