Respuesta :
Given:
Line a is perpendicular to line b .
Line a passes through the points (1,-8) and (9,-12) .
Line b passes through the point (-8, -16).
To find:
The equation of b.
Solution:
Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_a=\dfrac{-12-(-8)}{9-1}[/tex]
[tex]m_a=\dfrac{-12+8}{8}[/tex]
[tex]m_a=\dfrac{-4}{8}[/tex]
[tex]m_a=-\dfrac{1}{2}[/tex]
Product of slopes of two perpendicular lines is -1.
[tex]m_a\times a_b=-1[/tex]
[tex]-\dfrac{1}{2}\times a_b=-1[/tex]
[tex]b=2[/tex]
Slope of line b is 2.
If a line passing through a point [tex](x_1,y_1)[/tex] with slope m, then equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
Line b passing through (-8,-16) with slope 2. So, equation of line b is
[tex]y-(-16)=2(x-(-8))[/tex]
[tex]y+16=2(x+8)[/tex]
[tex]y+16=2x+16[/tex]
Subtract 16 from both sides.
[tex]y=2x[/tex]
Therefore, the equation of line b is [tex]y=2x[/tex].
