Write the equation of the line perpendicular to the line 2x+ 5y = 12 and passing through the point (-10,3)
Put equation in standard form
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First, identify slope ofthe line `2x + 5y =12`
by solving for y.
`y = (-2/5)x + 12/5` Slope is `-2/5` so slope of a line that is perpendicular will have a slope that is the opposite reciprocal. That makes the slope of the line equal to `5/2` .
Using point slope form of a line `y - y_(1) = m ( x -x_(1))`
where `(x_(1), y_(1))`
represents the point(-10, 3) and m represnets slope of: `(5/2)`
This gives: `y - 3 = 5/2 (x + 10)`
Rewrite in standard form by multiplying both sides by 2, then distributing the 2 and 5 and placing in form: `ax + by = c` ` `
`2(y - 3) = 5(x + 10)`
`2y - 6 = 5x + 50`
`5x -2y = -56` is the answer in standard form.
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