Question

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

Answer 1

See explanation

Explanation:

Given:`" " color(brown)(x-y=2)`

`color(green)("Step 1: Rearrange the equation into standard form")`

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

`color(brown)(x-ycolor(blue)(+y)=2color(blue)(+y))`

`=> x+0=2+y`

Subtract `color(blue)(2)` from both sides

`=>color(brown)(x color(blue)(-2)=2color(blue)(-2)+y)`

`=>x-2=0+y`

`color(green)(y=x-2)`

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

`color(green)("Step 2: Build data so that graph can be plotted")`
Selecting values for `x` at random

Let `x=-1" then "y=-1-2 = -3`

Let `x=0" then "y=0-2=-2`

Let `x=2" then "y=2-2=0`

We now have three sets of point

Point `P_1->(x,y)->(-1,-3)`
Point `P_2->(x,y)->(0,-2)`
Point `P_2->(x,y)->(2,0)`

Mark these point on graph paper and draw a line through them extending it to the edges of the scales. If all three dots must line up. If not then there is an error some where. 3 dots are better than just 2 as they form a check.

Your graph should look something like this: