Question

In what quadrant of the coordinate plane is the graph of the direct proportion located which is parallel to the graph, expressed by the formula:

Note: Please answer both questions in the same format (The direct proportion is ____. The graph is located on quadrants ___ and ___.).

Answer 1

Answer:

Part 1) The direct proportion is $y=0.8x$. The graph is located on quadrants I and III

Part 2) The direct proportion is $y=-0.4x$. The graph is located on quadrants II and IV

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 1) we have

$y=0.8x-1.6$

Remember that

If two lines are parallel, then their slopes are the same

In this problem, the slope of the given line is $m=0.8$

therefore

The direct proportion is $y=0.8x$

The graph is located on quadrants I and III

see the attached figure to better understand the problem

Part 2) we have

$y=-0.4+1$

Remember that

If two lines are parallel, then their slopes are the same

In this problem, the slope of the given line is $m=-0.4$

therefore

The direct proportion is $y=-0.4x$

The graph is located on quadrants II and IV

see the attached figure to better understand the problem

Answer 2

The direct proportion is 0.8.

The graph is located on quadrants first and second.

The direct proportion is -0.4.

The graph is located on quadrants second and fourth.

What is direct proportion?

The relation between quantities whose ratio is constant:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed as;

$\rm y= kx$

Where the constant of proportionality k is equal to the slope m of the line.

1. The given line is;

$\rm y=0.8x-1.6$

If two lines are parallel, then their slopes are the same then the slope of the other line is also m = 0.8.

The graph is located in quadrants I and III.

The direct proportion is 0.8.

The graph is located on quadrants first and second.

2.  The given line is;

$\rm y=-0.4x-1$

If two lines are parallel, then their slopes are the same then the slope of the other line is also m = -0.4.

The graph is located in quadrants I and III.

The direct proportion is -0.4.

The graph is located on quadrants second and fourth.

To know more about Direct variation click the link given below.

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