Writing Linear Equations in Point-Slope Form

To determine if Ron-Jon is correct or not, let's find the equation ourselves. Then, we need to find the slope. This can be done using the slope formula and Ron-Jon's two points. Now that we know the slope we can substitute it into the point-slope form. $$y-y_1=\text{-}\frac{1}{2}(x-x_1)$$ We can see that Ron-Jon got the correct slope so he might actually be correct with the equation. The second step for us is to substitute one of our points for $(x_1,y_1).$ However, let's try both to be able to compare with Ron-Jon's equation. $$\begin{array}{rl}y-4& =\text{-}\frac{1}{2}(x-(\text{-}3))\\ y-2& =\text{-}\frac{1}{2}(x-1)\end{array}$$ Thus, we have two versions of the equation in point-slope form and neither matches Ron-Jons equation. $$y-4=\text{-}\frac{1}{2}(x-1).$$ We can see that Ron-Jon used the $x$-value from one point and the $y$-value from another. This is wrong as you have to use the $x$- and $y$-coordinates from the same point. We have now found the error and the correct equations.