Respuesta :
3y=x-3
y=1/3x-1
Perpendicular slope: -3
y=-3x+b
Plug in the coordinates in the equation:
-9=-3(5)+b
-9=-15+b
4=b
Equation: y=-3x+4
Also, when finding the perpendicular slope you take the reciprocal of the original slope and make it negative if it is positive and make it positive if it’s negative.
y=1/3x-1
Perpendicular slope: -3
y=-3x+b
Plug in the coordinates in the equation:
-9=-3(5)+b
-9=-15+b
4=b
Equation: y=-3x+4
Also, when finding the perpendicular slope you take the reciprocal of the original slope and make it negative if it is positive and make it positive if it’s negative.
Equation of a line perpendicular to x - 3y = 3 will be y = -3x + 6.
If two lines having slopes [tex]m_1[/tex] and [tex]m_2[/tex] are perpendicular, property of perpendicular lines shows,
[tex]m_1\times m_2=-1[/tex]
Line given in the question is,
x - 2y = 3
-2y = 3 - x
[tex]y=\frac{1}{3}x-1[/tex]
Slope of this line is,
[tex]m_1=\frac{1}{3}[/tex]
Therefore, slope of the perpendicular line to the given line will be,
[tex]\frac{1}{3}\times m_2=-1[/tex]
[tex]m_2=-3[/tex]
Equation of a line passing through a point (h, k) and slope 'm' is given by,
y - k = m(x - h)
Therefore, equation of a line passing through (5, -9) and slope (-3) will be,
y - (-9) = -3(x - 5)
y + 9 = -3x + 15
y = -3x + 6
Hence, equation of the line perpendicular to x - 3y = 3 will be y = -3x + 6.
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