Express the following $$\sum _{ i=1 }^{ n }{ ({ \beta }_{ 1 }x_{ i }+{ \beta }_{ 0 }-y_{ i })^{ 2 } }$$
To become something of the form:
$∥Ax−b∥^{ 2 }$ where $A$ is an $m$−by−$n$ matrix and $b$ is an $m$−by−$1$ matrix. Note that $x$ is an $n$−by−$1$ matrix. We need to find explicitly $A$ and $b$ in terms of $x_{ 1 },...,x_{ n }$ and $y_{ 1 },...,y_{ n }$.
Try going the opposite direction: Starting with a matrices $A$ and $b$, with components $A_{i j}$ and $b_{i}$ respectively, what would that matrix norm look like when expressed in terms of components? What $A_{i j}$ and $b_i$ will then give you the form you want?