# How do you graph y=4x?

Apr 13, 2016

graph{y=4x [-10, 10, -5, 5]}

#### Explanation:

Graph $y = 4 x$
First, determine your slope and y-intercept.
(Your equation is in slope-intercept form)
Slope-intercept Form: $y = m x + b$
$m$ is the slope
$b$ is the $y$-intercept

In your equation, the slope is $4$ and the $y$-intercept is $0$.

Because your $y$-intercept is $0$, place your first point at $\left(0 , 0\right)$. Your second point should be at $\left(1 , 4\right)$ because the graph rises $4$ units for every $1$ unit is runs.

graph{y=4x [-10, 10, -5, 5]}

Apr 13, 2016

Take for x any two numbers. Let the x be 1 and 2.
So, according to the equation the results for the y would be as follows:
 y=4*1=4  so this is $\left(x , y\right) = \left(1 , 4\right) ,$and
$y = 4 \cdot 2 = 8 \implies \left(2 , 8\right)$

enter image source here

Apr 13, 2016

underline("Full explanation")" "# given about principle and method for this question.

#### Explanation:

The number in front of the $x$ is the gradient (slope). This number represents the amount of up or down for a given amount of along. This is determined reading from left to right.

The value of 4 is really $\frac{4}{1}$. This means that for 1 along you go up 4.

If the number in front of the x (coefficient) is positive the 'slope' goes up. If the coefficient is negative it means the 'slope' is down.

For this question; substitute any value you chose into $x$, multiply it by 4 and you have your value for y
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Let $x = 0 \to y = 4 \left(0\right)$

At $x = 0 \text{ we find that } y = 0$

So this can be our first point on the graph.

$\textcolor{b l u e}{{\text{Point}}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(0 , 0\right)}$
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Choosing a number at random: I chose 2

Let $x = 2 \to y = 4 \left(2\right)$

At $x = 2 \text{ we find that } y = 8$

So this can be our second point on the graph.

$\textcolor{b l u e}{{\text{Pont}}_{2} \to \left({x}_{2} , {y}_{2}\right) \to \left(2 , 8\right)}$
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Note that gradient $\to \left(\text{change in y axis")/("change in x axis}\right) \to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$= \frac{8 - 0}{2 - 0} \text{ " =" "8/2" "=" "4/1" }$ reading left to right.
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Mark your two points on the graph paper. Draw a line through them extending it to the edges of the axis.

$\textcolor{red}{\text{Label your axis "-> " extra marks}}$
$\textcolor{red}{\text{Label your graph" ->" extra marks}}$

The label could read something like:

"graph of $y = 4 x$"