Chapter 4: Q. 118 (page 452)

Graph the pair of equations in the same rectangular coordinate system :
$y = - \frac{1}{3} x$ and $y = - \frac{1}{3}$ .

Short Answer

Expert verified

The required graph is

Step by step solution

Given Information :

Given equations are, $y = - \frac{1}{3} x$ and $y = - \frac{1}{3}$ .

Plot graph for the equation y=-13x :

The first equation $y = - \frac{1}{3} x$ has both x and y. The y - values depend on the x - values, so the y - coordinate will change with respect to the x - values.

$x$	$y = - \frac{1}{3} x$	$(x, y)$
$- 2$	$y = - \frac{1}{3} \times (- 2) = \frac{2}{3}$	$(- 2, \frac{2}{3})$
$- 1$	$y = - \frac{1}{3} \times (- 1) = \frac{1}{3}$	$(- 1, \frac{1}{3})$
$0$	$y = - \frac{1}{3} \times 0 = 0$	$(0, 0)$
$1$	$y = - \frac{1}{3} \times 1 = - \frac{1}{3}$	$(1, - \frac{1}{3})$
$2$	$y = - \frac{1}{3} \times 2 = - \frac{2}{3}$	$(2, - \frac{2}{3})$

On plotting the points of the above table on the graph, we get a slanted line for the first equation,

Plot graph for the equation y=-13:

The second equation, $y = - \frac{1}{3}$ has a constant y-value for all the values of x.

$x$	$y = - \frac{1}{3}$	$(x, y)$
$- 2$	$y = - \frac{1}{3}$	$(- 2, - \frac{1}{3})$
$- 1$	$y = - \frac{1}{3}$	$(- 1, - \frac{1}{3})$
$0$	$y = - \frac{1}{3}$	$(0, - \frac{1}{3})$
$1$	$y = - \frac{1}{3}$	$(1, - \frac{1}{3})$
$2$	$y = - \frac{1}{3}$	$(2, - \frac{1}{3})$