   # Predict whether each of the following pairs of equations represents parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. Then graph each pair of lines to check your predictions. (The properties presented in Problem 83 should be very helpful. (a) 5.2 x + 3.3 y = 9.4 and 5.2 x + 3.3 y = 12.6 (b) 1.3 x − 4.7 y = 3.4 and 1.3 x − 4.7 y = 11.6 (c) 2.7 x + 3.9 y = 1.4 and 2.7 x − 3.9 y = 8.2 (d) 5 x − 7 y = 17 and 7 x + 5 y = 19 (e) 9 x + 2 y = 14 and 2 x + 9 y = 17 (f) 2.1 x + 3.4 y = 11.7 and 3.4 x + 2.1 y = 17.3 (g) 7.1 x − 2.3 y = 6.2 and 2.3 x + 7.1 y = 9.9 (h) − 3 x + 9 y = 12 and 9 x − 3 y = 14 (i) 2.6 x − 5.3 y = 3.4 and 5.2 x − 10.6 y = 19.2 (j) 4.8 x − 5.6 y = 3.4 and 6.1 x + 7.6 y = 12.3 ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 7.4, Problem 86PS
Textbook Problem
8 views

## Predict whether each of the following pairs of equations represents parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. Then graph each pair of lines to check your predictions. (The properties presented in Problem 83 should be very helpful.(a) 5.2 x + 3.3 y = 9.4 and 5.2 x + 3.3 y = 12.6 (b) 1.3 x − 4.7 y = 3.4 and 1.3 x − 4.7 y = 11.6 (c) 2.7 x + 3.9 y = 1.4 and 2.7 x − 3.9 y = 8.2 (d) 5 x − 7 y = 17 and 7 x + 5 y = 19 (e) 9 x + 2 y = 14 and 2 x + 9 y = 17 (f) 2.1 x + 3.4 y = 11.7 and 3.4 x + 2.1 y = 17.3 (g) 7.1 x − 2.3 y = 6.2 and 2.3 x + 7.1 y = 9.9 (h) − 3 x + 9 y = 12 and 9 x − 3 y = 14 (i) 2.6 x − 5.3 y = 3.4 and 5.2 x − 10.6 y = 19.2 (j) 4.8 x − 5.6 y = 3.4 and 6.1 x + 7.6 y = 12.3

To determine

(a)

To predict:

Whether the following pair of equations 5.2x+3.3y=9.4 and 5.2x+3.3y=12.6 represents parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

### Explanation of Solution

Approach:

To find whether the line Ax+By=C and Ax+By=C is parallel or perpendicular the following property is used.

For the line to be parallel the following property should be satisfied.

AA=BBCC

For the lines to perpendicular, the following property should be satisfied.

AA=BB

If none of the above two properties are followed then the line intersects each other but not perpendicular to each other.

Calculation

Consider the given equation

5.2x+3.3y=9.4

5.2x+3.3y=12.6

For the line to be parallel the following property should be satisfied.

AA=BBCC

Substitute 5.2 for A, 5.2 for A, 3.3 for B, 3.3 for B, 9.4 for C and 12.6 for C in the above property

To determine

(b)

To predict:

Whether the following pair of equations 1.3x4.7y=3.4 and 1.3x4.7y=11.6 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(c)

To predict:

Whether the following pair of equations 2.7x+3.9y=1.4 and 2.7x3.9y=8.2 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(d)

To predict:

Whether the following pair of equations 5x7y=17 and 7x+5y=19 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(e)

To predict:

Whether the following pair of equations 9x+2y=14 and 2x+9y=17 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(f)

To predict:

Whether the following pair of equations 2.1x+3.4y=11.7 and 3.4x+2.1y=17.3 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(g)

To predict:

Whether the following pair of equations 7.1x2.3y=6.2 and 2.3x+7.1y=9.9 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(h)

To predict:

Whether the following pair of equations 3x+9y=12 and 9x3y=14 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(i)

To predict:

Whether the following pair of equations 2.6x5.3y=3.4 and 5.2x10.6y=19.2 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

To determine

(j)

To predict:

Whether the following pair of equations 4.8x5.6y=3.4 and 6.1x+7.6y=12.3 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

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