Question

For what value of A will the lines represented by the following equations be parallel?

Y = 21x + 14
Y = 7(3x + A)
A. 9
B. 7
C. 6
D. 5

Answer 1

The lines will be parallel for A = 5. Therefore, the correct option is D. 5.

Step-by-step explanation:

To find out whether the given lines are parallel, we need to find the value of A for which the equations become equivalent. If the equations become equivalent, then the lines will be parallel.

Let's start with the second equation, Y = 7(3x + A). To make it equivalent to the first equation, Y = 21x + 14, we need to find the value of A for which the coefficients of x in both equations are equal.

The coefficient of x in the first equation is 21, and in the second equation, it is 21(3) = 63. So, we need to find A such that 63 = 21(3 + A). Simplifying this, we get:

A = -5

Now, let's check whether this value of A makes both equations equivalent. Substituting A = -5 in the second equation, we get:

Y = 7(3x - 5)

Simplifying this, we get:

Y = 21x - 35

Comparing this with the first equation, Y = 21x + 14, we can see that both equations have the same coefficient of x (21) and different constants (-35 and 14). This means that both equations represent parallel lines. Hence, our final answer is A = -5 or equivalently, A = 5 (since A is negative in our calculation). Therefore, the correct option is D. 5.