How do you graph the line `2x - 5y=10`?

Transpose (manipulate) the equation as follows:

Add `color(blue)(5y)` to both sides

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

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Subtract `color(blue)(10)` from both sides

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

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Divide both sides by `color(blue)(5)`

`color(brown)( (2x)/(color(blue)(5)) -10/(color(blue)(5)) = 5/(color(blue)(5)) xx x`

But `5/5=1`

`color(blue)(y=2/5 x-2)" "`This is standard form of the equation
`color(red)("=================================")`

The line crosses the y-axis ( `y_("intercept"` ) when `x=0`

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

So one point is:`" "(x,y)->(0,-2)`

`color(red)("Mark that point on the graph")`
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The line crosses the x-axis ( `x_("intercept")` ) at `y=0`

`0=2/5 x-2`

`=> 2 xx5/2=x = 5`

So the other point is:`" "(x,y)->(5,0)`
`color(red)("Mark that point on the graph")`
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`color(blue)("Draw a line through both these points and that is your graph.")`