Question

How do you graph `y=4x`?

Answer 1

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

Explanation:

Graph `y=4x`
First, determine your slope and y-intercept.
(Your equation is in slope-intercept form)
Slope-intercept Form: `y=mx+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 `(0,0)`. Your second point should be at `(1,4)` because the graph rises `4` units for every `1` unit is runs.

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

Answer 2

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 `(x,y)=(1,4),`and
`y=4*2=8 => (2,8)`
#
enter image source here

Answer 3

`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 `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
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let `x=0 -> y=4(0)`

At `x=0 " we find that "y=0`

So this can be our first point on the graph.

`color(blue)("Point"_1 -> (x_1,y_1)->(0,0))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Choosing a number at random: I chose 2

Let `x=2 ->y=4(2)`

At `x=2 " we find that "y=8`

So this can be our second point on the graph.

`color(blue)("Pont"_2->(x_2,y_2)->(2,8))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that gradient `->("change in y axis")/("change in x axis") -> (y_2 -y_1)/(x_2-x_1)`

`=(8-0)/(2-0)" " =" "8/2" "=" "4/1" "` reading left to right.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mark your two points on the graph paper. Draw a line through them extending it to the edges of the axis.

`color(red)("Label your axis "-> " extra marks")`
`color(red)("Label your graph" ->" extra marks")`

The label could read something like:

"graph of `y=4x`"