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## Main Question or Discussion Point

This exercise is located in the vector space chapter of my book thats why im posting it here.

Recently started with this kind of exercise, proof like exercises and Im a little bit lost

Proof that given a, b, c real numbers, the set X = {(x, y) E R^2; ax + by <= c} ´is convex at R^2

the definition of convex set in the book is given like that: u, v E X => [u, v] C X

and [u,v]={ (1-t)u+tv ; 0<=t<=1}

Didnt do much, just that :

u=(x1,y1) and ax1+by1<c

v=(x2,y2) and ax2+by2<c

and that [u,v]={(1-t)x1+tx2,(1-t)y1+ty2)}

Recently started with this kind of exercise, proof like exercises and Im a little bit lost

Proof that given a, b, c real numbers, the set X = {(x, y) E R^2; ax + by <= c} ´is convex at R^2

the definition of convex set in the book is given like that: u, v E X => [u, v] C X

and [u,v]={ (1-t)u+tv ; 0<=t<=1}

Didnt do much, just that :

u=(x1,y1) and ax1+by1<c

v=(x2,y2) and ax2+by2<c

and that [u,v]={(1-t)x1+tx2,(1-t)y1+ty2)}