could slope be calculated without a data table

Anon

You have to use the underscore not the caret  (hat)

$$gradient (slope)=\dfrac{y_2-y_1}{x_2-x_1}$$

I entered this using the LaTex tab        

gradient (slope)=\dfrac{y_2-y_1}{x_2-x_1}

Yes, as long as you have the coordinates, you can do slope=$${\frac{\left({{\mathtt{y}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{y}}}^{{\mathtt{1}}}\right)}{\left({{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{x}}}^{{\mathtt{1}}}\right)}}$$.