Given:
The equation of a first line is,
[tex]y=\frac{1}{8}x+2[/tex]
The objective is to find the equation of a second line perpendicular to the first line through the point (-8,0).
Explanation:
The general equation of straight line is,
[tex]y=mx+b[/tex]
Here, m represents the slope of the line and b represents the y-intercept.
To find slope of first line:
By comparing the general equation with the first line,
[tex]m_1=\frac{1}{8}[/tex]
To find slope of second line:
For perpendicular lines, the product of their slope values will be -1.
[tex]\begin{gathered} m_1\times m_2=-1 \\ \frac{1}{8}\times m_2=-1 \\ m_2=-8_{} \end{gathered}[/tex]
Since the second line passes throught the point(-8,0), the equation of the line can be calculated using slope point formula of straight line.
[tex]y-y_1=m_2(x-x_1)_{}[/tex]
To find equation of the perpendicular line:
Consider the given points as,
[tex](x_1,y_1)=(-8,0)[/tex]
On plugging the values in the above equation,
[tex]\begin{gathered} y-0=-8(x-(-8)) \\ y=-8(x+8) \\ y=-8x-64 \end{gathered}[/tex]
Hence, the equation of the perpendicular line is y = -8x - 64.
