Write an equation of the line in point slope form parallel to y=1/3x-5 through point (3,-7) Show work.

hmmm so, parallel lines have the same slope, so a line that's parallel to y=1/3x-5, will also have the same slope as that one, what would that be anyway?    [tex]\bf y=\stackrel{slope}{\cfrac{1}{3}}x-5[/tex] , well, low and behold, since that equation is in slope-intercept form already, we can see is just 1/3.

so, what is the equation of a line whose slope is 1/3 and runs through 3, -7?

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~ 3 &,& -7~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{1}{3} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-7)=\cfrac{1}{3}(x-3)\implies y+7=\cfrac{1}{3}(x-3)[/tex]