What method have you learned for finding a straight line?

I prefer the one which says $\displaystyle y - y_1 = m(x-x_1)$ where $\displaystyle (x_1,y_1)$ is a given coordinate and $\displaystyle m$ is the gradient.

To find the gradient use the equation $\displaystyle m = \dfrac{y_2 - y_1}{x_2 - x_1}$ where $\displaystyle (x_1,y_1) \text{ and } (x_2,y_2)$ are two points on the line. As long as you are consistent with which point is 1 and which is 2 the order does not affect the answer which you found out in the OP.

In this question we have the points (5,3) and (-7,7). Using the equation above [(-7,7) is (x_1,y_1) here] we work out the gradient $\displaystyle \dfrac{3-7}{5-(-7)} = \dfrac{-4}{12} = -\dfrac{1}{3}$.

Now we know that $\displaystyle m = -\dfrac{1}{3}$ we can sub it in to the equation of a line using either of our coordinates. I shall choose (5,3) as it contains no negative numbers

$\displaystyle y - 3 = -\dfrac{1}{3}(x - 5)$ and upon adding three to both sides: $\displaystyle y = 3 - \dfrac{1}{3}(x-5)$

it is up to you to arrange that into the form $\displaystyle y=mx+c$

edit: perhaps

Wolfram will be of use as a visual aid

btw: if you don't use latex can you just use plain text with brackets please? Your working is almost impossible to read. (y2-y1)/(x2-x1) = m is much easier!