Find the equations of lines with a specific slope that form a triangle of a given area with the coordinate axes.

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Lines Forming a Triangle of Given Area with Coordinate Axes

Lines, circles and conics warmup

Find equations of the lines of slope \( -\frac{3}{4} \) that form with the coordinate axes a triangle of area 24 square units.

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What you need first

Equation of a straight line
Finding x- and y-intercepts
Area of a triangle

What this problem tests

Tests the ability to relate the algebraic equation of a line to the geometric properties of the figure it forms with the coordinate axes.

This is a standard analytic geometry problem often found in precalculus or early calculus courses to test understanding of linear equations and geometric properties on the Cartesian plane.

Lines Forming a Triangle of Given Area with Coordinate Axes

What you need first

What this problem tests

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