The equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x-9 is y = -2x + 24
The given equation is:
\(y = \frac{1}{2}x - 9\)
Comparing \(y = \frac{1}{2}x - 9\) with y = mx + c
The slope, m = 1/2 = 0.5
The equation of the line perpendicular to y = mx + c and passing through the point (x₁, y₁) is:
\(y - y_1 = \frac{-1}{m}(x - x_1)\)
The line passes through the point (7, 10)
That is, x₁ = 7, y₁ = 10
Substitute x₁ = 7, y₁ = 10 and m = 0.5 into the equation \(y - y_1 = \frac{-1}{m}(x - x_1)\)
\(y - 10 = \frac{-1}{0.5} (x-7)\\\\y - 10 = -2(x - 7)\\\\y - 10 = -2x + 14\\\\y = -2x + 14 + 10\\\\y = -2x + 24\)
The equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x-9 is y = -2x + 24
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