Question

How do you graph `y= x - 3`?

Answer 1

See description

Explanation:

In straight line graphs it is better to determine 3 points as the third point acts as a check. They should all line up.

Determine point 1`->P_1->(x_1,y_1)`

Let `x=0` giving `y=0-3 => y=-3`

So `color(blue)(P_1->(x_1,y_1)->(0,-3))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Determine point 2`->P_2->(x_2,y_2)`

Let `y=0` giving `0=x-3`

Add 3 to both sides

`=>0+3=x-3+3`

But -3+3=0#

`x=3`

So `color(blue)(P_2->(x_2,y_2)->(3,0)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Determine checking point 3`->P_3->(x_3,y_3)`

I chose an `x` value of 5 giving

`y=5-3=+2`

So `color(blue)(P_3->(x_3,y_3)->(5,2))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mark the points and draw a straight line through extending it to the edge of the squared area on the paper.

`color(brown)("Don't forget to label your points and write a title to your graph")`
`color(brown)("For example: Graph of "y=x-3" This gets you extra marks.")`
`color(brown)("You must label your axis as well!")`