Question

Determine the shape of graph for the equation $y=4x$ by plotting it in the cartesian plane.

• A. Circle
• B. Straight line
• C. Parabola
• D. Hyperbola

Answer 1

The correct option is B Straight line

Given, $y=4x$

Concept: To draw the shape of this equation, find the different values of $y$ by substituting different coordinates of $x$ as stated in the following table. plot all the coordinates$(x,y)$ on the cartesian plane.

Step 1: Take some random values of $x$ as shown in table:

x	y
0	?
1	?
2	?
-1	?
-2	?

Step 2: Substituting the values of $x$ in $y=4x$ to find $y$:
$\bullet$ For $x=0,y=4\times 0\Rightarrow y=0$
$\bullet$ For $x=1,y=4\times 1\Rightarrow y=4$
$\bullet$ For $x=2,y=4\times 2\Rightarrow y=8$
$\bullet$ For $x=-1,y=4\times -1\Rightarrow y=-4$
$\bullet$ For $x=-2,y=4\times -2\Rightarrow y=-8$

From the above calculations, we get:

x	y	Ordered Pair
0	0	$(0,0)$
1	4	$(1,4)$
2	8	$(2,8)$
-1	-4	$(-1,-4)$
-2	-8	$(-2,-8)$

Step 3: Plot all the ordered pairs on the cartesian plane.
Step 4: Join all these points.
We can connect all these ordered pairs through a straight line.
Hence, the shape of the equation $y=4x$ is a straight line.
Option (b) is correct.