Como você representa graficamente a linha 2x - 5y = 10 2x5y=10?

Transponha (manipule) a equação da seguinte maneira:

Adicionar color(blue)(5y)5y para os dois lados

color(brown)(2x-5ycolor(blue)(+5y)=10color(blue)(+5y))" "->" "2x+0=10+5y2x5y+5y=10+5y 2x+0=10+5y

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtrair color(blue)(10)10 de ambos os lados

color(brown)(2xcolor(blue)(-10)=10color(blue)(-10)+5y)" "->" "2x-10=0+5y2x10=1010+5y 2x10=0+5y

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Divida os dois lados por color(blue)(5)5

color(brown)( (2x)/(color(blue)(5)) -10/(color(blue)(5)) = 5/(color(blue)(5)) xx x2x5105=55×x

Mas 5/5=155=1

color(blue)(y=2/5 x-2)" " y=25x2 Esta é a forma padrão da equação
color(red)("=================================")=================================

A linha cruza o eixo y ( y_("intercept"yintercept ) quando x=0x=0

so y_("intercept")= 2/5 (0)-2 = -2yintercept=25(0)2=2

Então, um ponto é:" "(x,y)->(0,-2) (x,y)(0,2)

color(red)("Mark that point on the graph")Mark that point on the graph
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A linha cruza o eixo x ( x_("intercept")xintercept ) a y=0y=0

0=2/5 x-20=25x2

=> 2 xx5/2=x = 52×52=x=5

Então, o outro ponto é:" "(x,y)->(5,0) (x,y)(5,0)
color(red)("Mark that point on the graph")Mark that point on the graph
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Draw a line through both these points and that is your graph.")Draw a line through both these points and that is your graph.

Tony B