Question

Determine the shape of graph for the equation $y=3x-1$ by plotting it in the cartesian plane.

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

Answer 1

The correct option is C Straight line

Given, $y=3x-1$

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 $y=3x-1$ to find $y$:
$\bullet$ For $x=0,y=3\times 0-1\Rightarrow y=-1$
$\bullet$ For $x=1,y=3\times 1-1\Rightarrow y=2$
$\bullet$ For $x=2,y=3\times 2-1\Rightarrow y=5$
$\bullet$ For $x=-1,y=3\times (-1)-1\Rightarrow y=-4$
$\bullet$ For $x=-2,y=3\times (-2)-1\Rightarrow y=-7$

From the above calculations, we get:

x	y	Ordered pair
0	-1	$(0,-1)$
1	2	$(1,2)$
2	5	$(2,5)$
-1	-4	$(-1,-4)$
-2	-7	$(-2,-7)$

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 $y=3x-1$ is a straight line.
Option (c) is correct.