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 $A \geq 0$.)

Solution

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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