Find the slope-intercept equation of a line passing through a given point and perpendicular to a given line.

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Equation of a Perpendicular Line

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Find the slope-intercept equation of the line \(M\) through \((1, 4)\) that is perpendicular to the line \(L\) with equation \(2x - 6y = 5\).

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What you need first

Solving linear equations for a specific variable
Understanding the relationship between slopes of perpendicular lines
Substituting a point into a linear equation to find the y-intercept

What this problem tests

Tests the ability to convert a linear equation to slope-intercept form, apply the perpendicular slope condition, and solve for the y-intercept using a given point.

This is a fundamental problem in coordinate geometry, often encountered in precalculus and early calculus courses as a prerequisite skill.

Equation of a Perpendicular Line

What you need first

What this problem tests

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