Respuesta :
You have the following equation of a line:
[tex]y=-\frac{1}{2}x+11[/tex]In order to find the equation of a line perpendicular to the previous one, you take into account that the relation between the slopes of both lines is as follow:
[tex]m_{1\cdot}m_2=-1[/tex]You have that the slope of the first line is m1 = -1/2. By using the previous equation you can find the slope of the second slope, just as follow:
m₂ = -1/(m₁) = -1/(-1/2) = 2
In order to find the equation of the second line, you use the following formula:
m₂ = (y - yo)/(x - xo)
where m2 is the slope of the second line, and (xo,yo) is a point with specific coordinates. You have that the second line passes trough the point (-10,1), then, by replacing into the last expression, you can solve for m, just as follow:
m₂ = (y - 1)/(x - (-10))
m₂ = (y - 1)/(x + 10)
(x + 10) m₂ = y - 1
m₂x + 10m₂ + 1 = y
(2)x + 10(2) + 1 = y
2x + 20 + 1 = y
2x + 21 = y
Hence, the equation of the second line is:
y = 2x + 21
