Question

Translate the algebraic statments into words: y=2x+5 and y=6x+5

Answer 1

Answer:

• 1)  For y = 2x + 5, the answer is "y is the double of x increased by 5"

• 2) For y = 6x + 5, the answer is "y is the six times x increased by 5"

• 3) For the question about figure 0 for each pattern, the answer is "for both, there are 5 units of y when there are 0 units of x".

Explanation:

In the real world patterns and relationships are expressed with words.

Some of those relations or patterns are complex and enclose unknown facts, questions or problems that you might want to elucidate. When those relationships can be translated into algebraic statements the solution to the such questions or problems may be systematic an easier. Thus, translating verbal statements into algebraic expresssions and viceversa is a very important mathematical skill.

Here, you need to understand what the algebraic expressions represent in words.

1. y = 2x + 5

As you can see the variable x is multiplied by two and after the multiplication a constant, 5 is added. Thus, a good translation for that statement into words would be:

• y is the double of x increased by five

2. y = 6x + 5

In this case the variable x is multiplied by six ant then 5 is added.

A good translation would be:

• y is six times x increased by 5.

3. What do you know about figure 0 for each pattern?

As for the question about about figure 0 for each pattern, you just replace x with zero and get the answer:

• y = 2x + 5 ⇒ y = 2(0) + 5 = 0 + 5 = 5

• y = 6x + 5 = 6(0) + 5 = 0 + 5 = 5

Hence, both patterns show that there are 5 units of y when there are zero units of x (depending onwhat y represents, it might be tiles, cars, money, whatever the pattern accounts for).