How do you graph #x+2y=10# by plotting points?

Given#" "x+2y=10#

changing the formula so that it is in standard form

Subtract #x# from both sides giving

#" "2y=10-x#

Divide both sides by 2 so that we have #y# on its own.

#" "y=5-x/2#
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This graph can be drawn if only two points are known but it is better to do 3 as a check to see if there is an error in your calculation. No error would mean that all the points line up. If not then check you calculations.

#color(blue)("First point")#

I chose the point where the graph crosses the x-axis
( x intercept ). To do this set #y=0#

#" "0=5-x/2# From this we observe that #x=10#

#color(blue)("Point 1 "-> (x,y)->(10,0))#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Second point")#

I chose the point where the graph crosses the y-axis (y intercept).
To do this we set #x=0#

#" "y=5-0/2# From this we observe that #y=5#

#color(blue)("Point 2 "-> (x,y)->(0,5))#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Third point")#

#"I choose "color(blue)(x=2)#

Substitute this in our equation and we have

#color(brown)(y=5-x/2 -> )color(green)( y= 5-(color(blue)(2))/2#

#color(blue)(y=+4 ) #

#color(blue)("Point 2 "-> (x,y)->(2,4))#
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#color(magenta)("Do not forget the extend the line to the edges of the graph.