A Constant Sum Equation

Geometry Level 1

Consider the collection of points such that the sum of each point's coordinates is 1. The graph of these points in the coordinate plane forms what shape?

A line A hyperbola A parabola A circle An ellipse Another different function

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Mateo Matijasevick by Mateo Matijasevick , 22, Colombia

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2 solutions

Let A = { ( x , y ) ∈ ℜ 2 ∣ x + y = 1 } A=\left\{ (x,y)\in { \Re }^{ 2 }|\quad x+y=1 \right\} . Clearly, this is the equation of a line.

14 Helpful 1 Interesting 2 Brilliant 7 Confused
Daniel Abib
Mar 12, 2020

We can write an equation for the problem as:

x + y = 1 x + y = 1

If we solve the equation for y, we have:

y = − x + 1 y = -x + 1

Which is an equation of a line with slope = -1, and y-intercept = 1.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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