Question

How do you graph the line `y=-3x+3`?

Answer 1

Wee explanation

Explanation:

`color(blue)("Main Method :")`

Determine 2 separate points which are marked on the graph paper then draw a line through them.
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`color(purple)("Method 1")`

Substitute any sensible values into `x` and se what value of `y` you get. Then plot the points with a line going through them.

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`color(purple)("Method 2 - more about teaching algebra")`

`color(blue)("Determine the point where "x=0)`

Substitute 0 wherever `x` is

`y=-3x+3" "->" "y=-3(0)+3`

but `0xx(-3)=0` giving:

`y=0+3`

So at `x=0" "y` takes on the value of 3

So point 1 `->P_1->(x,y)=(0,3)`
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`color(blue)("Determine the point where "y=0)`

Substitute 0 wherever `y` is:

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

Add `3x` to both sides

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

but `-3x+3x=0`

`3x=0+3`

Divide both sides by 3

`3/3x=3/3`

But `3/3=1`

`x=1`

So point 2 `->P_2->(x,y)=(1,0)`
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