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Write the standard form equation of the line passing through 4 9 and perpendicular to 2x minus 3y equals 7?
Thegrahamcracker
With a line in the form y = mx + c, it has gradient m and the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m.
A line through a point (x0, y0) with gradient m' has an equation of:
y - y0 = m' (x - x0)
which can be rearranged to a form for y = mx + c.
Thus for the line 2x - 3y = 7:
2x - 3y = 7
→ 3y = 2x + 7
→ y = 2/3 x + 7/3
→ it has gradient 2/3 → perpendicular line has gradient -3/2
→ perpendicular line through (4, 9) perpendicular to 2x - 3y = 7 has equation:
y - 9 = (-3/2)(x - 4)
→ 2y - 18 = -3(x - 4)
→ 2y - 18 = -3x + 12
→ 2y = 30 - 3x
→ 3x + 2y = 30
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