This equation is the slope form of the line with slope 5 going through the point (1, -2). Since the line has the correct slope, we should still check to see if this is an alternate way to represent the given line.

To do this we need to check whether (-1, 2) is on the line $\displaystyle{y}+{2}={5}{\left({x}-{1}\right)}.\usepackage{cmbright}\Huge\$ Replacing x with -1 and y with 2, $\displaystyle{y}+{2}={2}+{2}={4},\usepackage{cmbright}\Huge\$ but $\displaystyle{5}{\left({x}-{1}\right)}={5}{\left(-{1}-{1}\right)}={\left({5}-{2}\right)}=-{10},\usepackage{cmbright}\Huge\$ so $\displaystyle{y}+{2}\ne{5}{\left({x}-{1}\right)}\usepackage{cmbright}\Huge\$ when $\displaystyle{x}=-{1}\usepackage{cmbright}\Huge\$ and $\displaystyle{y}={2}.\usepackage{cmbright}\Huge\$