Write equation for a line that passes through (-2,4) and (4,1)

First find the slope of the line, which uses the formula: 

 

$${\frac{\left({\mathtt{y2}}{\mathtt{\,-\,}}{\mathtt{y1}}\right)}{\left({\mathtt{x2}}{\mathtt{\,-\,}}{\mathtt{x1}}\right)}}$$

 

= $${\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{4}}\right)}{\left({\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$$

= -3/6

=-1/2

 

Then plug in a point and the slope, $${\mathtt{m}}$$, into the point-slope formula:

 

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

$$\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{4}}\right) = {\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)\right)$$

Move the -4 to the right side:

$${\mathtt{y}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}$$

 

Simplify:

$${\mathtt{y}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}$$