Chapter 4: Q. 117 (page 452)

Graph the pair of equations in the same rectangular coordinate system :
$y = - \frac{1}{2} x$ and $y = - \frac{1}{2}$ .

Short Answer

Expert verified

The required graph is

Step by step solution

Given Information :

Given equations are, $y = - \frac{1}{2} x$ and $y = - \frac{1}{2}$ .

Plot graph for the equation y=-12x:

The first equation, $y = - \frac{1}{2} x$ 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.

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

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=-12:

The second equation $y = - \frac{1}{2}$ has a constant y-value for all the values of x.

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

On plotting the points of the above table on the graph, we get a straight horizontal line for the second equation,

Combine the two graphs :

On combining the graphs of given pair of equations, we get,

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Graph the pair of equations in the same rectangular coordinate system :
$y = - \frac{1}{2} x$ and $y = - \frac{1}{2}$ .

Short Answer

Step by step solution

Given Information :

Plot graph for the equation y=-12x:

Plot graph for the equation y=-12:

Combine the two graphs :

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Graph the pair of equations in the same rectangular coordinate system :y=-12xand y=-12.

Short Answer

Step by step solution

Given Information :

Plot graph for the equation y=-12x:

Plot graph for the equation y=-12:

Combine the two graphs :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Graph the pair of equations in the same rectangular coordinate system :
$y = - \frac{1}{2} x$ and $y = - \frac{1}{2}$ .