The slopes of two lines are 5 and 1/5 (1 over 5) . because of this, we can conclude that these two lines are which of the following? a) parallel b) perpendicular c) vertical d) none of these

A) Parallel lines have the same slope. 5 and 1/5 are not equal, so they are not parallel.

b) Perpendicular lines have negative reciprocal slopes. That means when you multiply the slopes together, you get -1. Let's try our slopes. 5 * 1/5 = 1, not -1, so these slopes are not negative reciprocals, and the lines are not perpendicular.

c) A vertical line has undefined slope since the slope of a vertical line involves division by zero. Here, the two lines have well defined slopes. The lines are not vertical.

d) This is the only choice left, so it is the answer.

The constant of proportionality is the value of the ratio of the two proportional quantities.

Explanation:

Two quantities are proportional or have a direct proportional relationship if their quotient, also called ratio, is constant.

In such a case you can write:

Amount of x / amount of y = constant, or simply:

Where the notation x / y is the ratio and k is the constant of proportionality.

From that expresssion, it is proved that when two quantities are proportional, if one doubles the other also doubles, if one quadruples the other also quadruples, and in general, if one is multiplied by a factor the other is multiplied by the same factor;

For example, the number of pencils and the number of boxes of pencils are proportional because:

12 pencils / 1 box = 1224 pencil / 2 box = 1248 pencil / 4 box = 12120 pencils / 10 boxes 12

The constant of proportionality is 12, indicating that each box contains 12 pencils; thus, both quantities (number of pencils and number of boxes of pencils) have a constant ratio of 12.