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

(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.

Approach:

To find whether the line Ax+By=C and A′x+B′y=C′ is parallel or perpendicular the following property is used.

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

AA′=BB′≠CC′

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′=BB′≠CC′

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

(b)

To predict:

Whether the following pair of equations 1.3x−4.7y=3.4 and 1.3x−4.7y=11.6 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

(c)

To predict:

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

(d)

To predict:

Whether the following pair of equations 5x−7y=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.

(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.

(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.

(g)

To predict:

Whether the following pair of equations 7.1x−2.3y=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.

(h)

To predict:

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

(i)

To predict:

Whether the following pair of equations 2.6x−5.3y=3.4 and 5.2x−10.6y=19.2 represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular and then plot the graph to check the prediction.

(j)

To predict:

Whether the following pair of equations 4.8x−5.6y=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.