Answer:
[tex]y = (-3/2)\, x + (-2)[/tex].
Step-by-step explanation:
If [tex](x_{0},\, y_{0})[/tex] is on the equation of the line [tex]y = m\, x + b[/tex], then substituting [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex] into the equation would still give an equality: [tex]y_{0} = m\, x_{0} + b[/tex].
In this question, since [tex](-2,\, 1)[/tex] is a point on the line [tex]y = m\, x + b[/tex], equality shall still hold after substituting in [tex]x = (-2)[/tex] and [tex]y = 1[/tex]:
[tex]1 = m\times (-2) + b[/tex].
Similarly, since [tex](2,\, -5)[/tex] is a point on this line, equality shall still hold after substituting in [tex]x = 2[/tex] and [tex]y = (-5)[/tex]:
[tex](-5) = m\times 2 + b[/tex].
The unknowns of both equations are [tex]m[/tex] and [tex]b[/tex].
Solve this system of two equations and two unknowns:
[tex]\left\lbrace\begin{aligned}& (-2)\, m + b = 1\\ & 2\, m + b = (-5)\end{aligned}\right.[/tex].
[tex]\left\lbrace\begin{aligned}& m = -\frac{3}{2} \\ & b = -2\end{aligned}\right.[/tex].
Therefore, the equation of this line would be:
[tex]y = (-3/2)\, x + (-2)[/tex].
