Given:
The point (-5, 2).
The line,
[tex]y=\frac{1}{2}x+3[/tex]
To find the equation of the line through (-5,2) and perpendicular to the above line:
Since, the slope of the above line is,
[tex]m=\frac{1}{2}[/tex]
So, the perpendicular slope is,
[tex]m_1=-2[/tex]
Using point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]
So, we get
[tex]\begin{gathered} y-2=-2(x-(-5)) \\ y-2=-2(x+5) \\ y-2=-2x-10 \\ y=-2x-10+2 \\ y=-2x-8 \end{gathered}[/tex]
Hence, the slope intercept form of the line is,
[tex]y=-2x-8[/tex]
