Write an equation of the line perpendicular to the given...

Write an equation of the line perpendicular to the given line and containing the given point. Write the answer in slopeintercept form or in standard form, as indicated.
$x+3 y=18 ;(4,2) ;$ standard form

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Key Concepts

Slope

The slope represents the rate of change between two variables, indicating how steep a line is. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

Perpendicular Lines

Lines are perpendicular when the product of their slopes equals -1. This means that if one line has a slope of m, any line perpendicular to it will have a slope of -1/m, provided m is not zero.

Point-Slope Form

The point-slope form of a linear equation, expressed as y - y? = m(x - x?), is useful when you know the slope of the line and a specific point through which the line passes. It provides a straightforward method to write the equation of a line.

Standard Form of a Linear Equation

Standard form is a way of writing a linear equation as Ax + By = C, where A, B, and C are integers and A is non-negative. Converting an equation to this form is common in many algebraic problems and facilitates certain types of analysis and comparison.

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