what is the equation of a line for (4,3) and (5,6)

First, you would need to find the slope of the line. 

Use the formula  $${\mathtt{m}} = {\frac{\left({\mathtt{x1}}{\mathtt{\,-\,}}{\mathtt{x2}}\right)}{\left({\mathtt{y1}}{\mathtt{\,-\,}}{\mathtt{y2}}\right)}}$$

Plug in the points: 

$${\mathtt{m}} = {\frac{\left({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}{\left({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{4}}\right)}}$$

m=3

 

Now use the slope and a point to write the equation in point-slope form:

$$\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{y1}}\right) = {m}{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{x1}}\right)}$$

$${\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{3}} = {\mathtt{3}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{4}}\right)$$

Simplify it:

y= 3x-12+3

 

y= 3x-9