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

Mar 2, 2017

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 $x$

$\textcolor{b l u e}{\text{Choosing substitution}}$ ( I am using just two points as this is a demo.)

Calculation Point 1 $\left({P}_{1}\right)$

Let ${x}_{1} = 2$

${y}_{1} = 4 \left(2\right) - 1 = 7 \text{ " ->" "P_1" } \to \left({x}_{1} , {y}_{1}\right) = \left(2 , 7\right)$

Calculation Point 2 $\left({P}_{2}\right)$

Let ${x}_{2} = - 2$

${y}_{2} = 4 \left(- 2\right) - 1 = - 9 \text{ "->P_2" } \to \left({x}_{2} , {y}_{2}\right) = \left(- 2 , - 9\right)$

$\textcolor{red}{\text{Notice that point "P_2" is the left most one}}$

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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$\textcolor{b l u e}{\text{Critical point}}$

You either need a given point or the equation.

Given equation:$\text{ } y = 4 x - 1$

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: $\left(x , y\right) \to \left(0 , - 1\right)$

Set $y = 0 \text{ : "y=4x-1" "->" "0=4x-1 " "->" } x = \frac{1}{4}$

So we now have a second point:$\left(x , y\right) \to \left(\frac{1}{4} , 0\right)$