Question

what is the shortest distance between the line y=1/2x+3 and point (-3,-3)

Answer 1

what do you think?

Answer 2

so, in short you're been really asked is
"what is the equation of a line that is perpendicular to y=1/2x+3 and passes through (-3,-3)" ?

so since you've done slopes, you get such equation

then you'd have 2 equations, one for each line
thus a system of equations

recall that in a system of equations, the solution is where the graphs meet or intersect

so the these two lines will intersect at a point on the 1st line, the given one

then you'd have 2 points

the solution to the system of equations, and (-3,3)

well, to find how long that is, use the distance formula \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ \square }}\quad ,&{\color{blue}{ \square }})\quad &({\color{red}{ -3}}\quad ,&{\color{blue}{ 3}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)