keeping in mind that perpendicular lines have negative reciprocal slopes, so hmmm wait a second, what is the slope of 2y=8x−6. anyway?


so, we're really looking for the equation of a line whose slope is -1/4 and runs through (-3, 3).
![\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})~\hspace{10em}slope = m\implies -\cfrac{1}{4}\\\\\\ \begin{array}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-3=-\cfrac{1}{4}[x-(-3)]\implies y-3=-\cfrac{1}{4}(x+3)\\\\\\y-3=-\cfrac{1}{4}x-\cfrac{3}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{4}+3\implies y=-\cfrac{1}{4}x+\cfrac{9}{4}](https://img.qammunity.org/2019/formulas/mathematics/middle-school/qx8yt3dz2xito1jdapw50zmf6raz3o127y.png)
now, that equation is fine, is in slope-intercept form, and we can do away with the denominators by simply multiplying both sides by the LCD of all fractions, in this case , 4, and put the equation in standard form instead.
standard form for a linear equation means
- all coefficients must be integers
- only the constant on the right-hand-side
- "x" must not have a negative coefficient
