Questions: Find the equation of the line. Through (12,-13); perpendicular to y=10. The equation is . (Type your answer in standard form, using integer coefficients with A ≥ 0.)

Find the equation of the line. Through (12,-13); perpendicular to y=10. The equation is . (Type your answer in standard form, using integer coefficients with A ≥ 0.)
Transcript text: Find the equation of the line. Through $(12,-13)$; perpendicular to $y=10$. The equation is $\square$ . (Type your answer in standard form, using integer coefficients with $A \geq 0$.)
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Solution

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Solution Steps

Step 1: Identify the Type of Line

The given line is \( y = 10 \), which is a horizontal line. A line perpendicular to a horizontal line is a vertical line.

Step 2: Determine the Equation of the Vertical Line

A vertical line passing through a point \((x_1, y_1)\) has the equation \( x = x_1 \). Given the point \((12, -13)\), the equation of the line is \( x = 12 \).

Step 3: Express the Equation in Standard Form

The standard form of a line is \( Ax + By = C \). For a vertical line \( x = 12 \), this can be expressed as: \[ 1x + 0y = 12 \] where \( A = 1 \), \( B = 0 \), and \( C = 12 \).

Final Answer

The equation of the line is \(\boxed{x = 12}\).

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