Question

How do you graph `y=4x-1` by plotting points?

Answer 1

See explanation

Explanation:

For a strait line graph you technically only need two points. It is better to have 3 or more. I would suggest 3. The logic behind this is that if all the points do not line up when you draw a line through them then you have a wrong calculation some ware.

You may chose to determine what is called critical points and use those (just 2) or you may chose substituting values for `x`

`color(blue)("Choosing substitution")` ( I am using just two points as this is a demo.)

Calculation Point 1 `(P_1)`

Let `x_1=2`

`y_1=4(2)-1 = 7" " ->" "P_1" "->(x_1,y_1)=(2,7)`

Calculation Point 2 `(P_2)`

Let `x_2=-2`

`y_2=4(-2)-1=-9" "->P_2" "->(x_2,y_2)=(-2,-9)`

`color(red)("Notice that point "P_2" is the left most one")`

You always read left to right on the x-axis. Sometimes the reverse order is given in questions setting 'a trap'.

ALWAYS READ LEFT TO RIGHT ON THE X-AXIS FOR WHEN Y IS THE ANSWER
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`color(blue)("Critical point")`

You either need a given point or the equation.

Given equation:`" "y=4x-1`

The x-axis crosses the y-axis at `x=0`
The y-axis crosses the x-axis at `y=0`

Set #x=0" : " y=4x-1" "->" "y=4(0)-1 " "->" "y=-1

So we now have the point: `(x,y)->(0,-1)`

Set `y=0" : "y=4x-1" "->" "0=4x-1 " "->" "x=1/4`

So we now have a second point:`(x,y)->(1/4,0)`