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`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(magenta)("Do not forget the extend the line to the edges of the graph.