The graph of y = 4x is a line which is

The value of #y# is the result of assigning a value to #x#, multiplying that value by 4. The answer is 'what #y# is worth'.

#"Point"_1" For "x=2;" " y=4xx2" "=" "8#

#"Point"_2" For "x=6;" "y=4xx 6" "=" "24#

#"Point"_3" For "x=0;" "y= 4 xx 0" " =" "0#

Consider point 1

Find on the x-axis the value of +2. Draw a very light line vertically.
Look along the y-axis until you find the point +8. Draw a very light line horizontally. Where the two lines meet is the point.

Repeat this process for one other value. Draw a line through the two points and that is your graph.

Important: Label your axis and put a title on your graph. You could right 'The graph of y=4x' This action will get you extra marks.

Your graph should look something like this

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#"

Algebra Examples

Step 1

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is , where is the slope and is the y-intercept.

Find the values of and using the form .

The slope of the line is the value of , and the y-intercept is the value of .

Slope:

y-intercept:

Step 2

Any line can be graphed using two points. Select two values, and plug them into the equation to find the corresponding values.

Create a table of the and values.

Step 3

Graph the line using the slope and the y-intercept, or the points.

Slope:

y-intercept:

Answer

Verified

Hint: In the given question, we have an equation in two variables. We have to plot the line on a graph which forms from this equation. Firstly convert the given equation to slope intercept form. From there, we find out the value of slope and the y- intercept. We plot a point at the y-intercept on y-axis. From there, we move up or down and then right or left depending upon the coefficient of x and y respectively, and join the points to form the line.

Complete step by step solution:
We have been given an equation y = 4x.
Clearly, this equation is of the type y = mx + c, hence, is already in the slope-intercept form.
Thus, slope m = 4 and, y-intercept c = 0
Hence, one point on the graph can be taken as (0,0).
Now,
$m=\dfrac{\text{coefficient of x }}{\text{coefficient of y } }$
Hence, we move up 1 (coefficient of y) points and then move to the right 4 (coefficient of x) points.
Thus, the second point is (0 + 1, 0 + 4) = (1, 4).
Now, we plot the two points and join them and we have our line.

Note: In this question, we only need to know how to get the points for the graph and then, how to plot the points on the graph. Then we just calculate the values from the equation, plot them on the graph, join the points on the graph and we get the line which marks the required equation.

How is the graph of y 4x is a line passing through origin?

What is the equation of this line Y 4x?

What is the slope of the line with the equation of Y =

What does Y 4x mean?