I have the answer, but I am stuck in the middle of the problem
Through (4,2) and (1,3)
m= 3 - 2 / 1 - 4 = - 1/3
y - 2 = (-1/3)x (x-4)
y - 2 = this is where I get stuck. I know the answer is y = (-1/3)x + 11/3
I get a different answer.
The general form is:
$\displaystyle y - y_1= m(x-x_1)$
Substituting values:
$\displaystyle y-2 = -\frac13 ( x - 4)$
Opening the bracket:
$\displaystyle y-2 = -\frac13x + \frac43$
Adding $\displaystyle 2$ to both sides:
$\displaystyle y = -\frac13 + \frac{10}{3}$
$\displaystyle \Delta y = \frac{1}{16} - \frac{5}{3} = -\frac{77}{48}$
$\displaystyle \Delta x = 3 - \frac12 = \frac52$
$\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{-\frac{77}{48}}{\frac52}$
$\displaystyle m = -\frac{77}{48} \div {\frac52} = -\frac{77}{48} \times \frac{2}{5} = -\frac{77}{120}$
Your gradient is $\displaystyle m = -\frac{77}{120}$
Use your normal apprach to find the equation. Substitute appropriate number into the general form, $\displaystyle y - y_1 = m(x-x_1)$.
EDIT: Sammyj, is your question posted correctly? The gradient is different to the answer that you posted.