Equivalent expressions are expressions with the same value. The following expressions are equivalent
- [tex]p =5d + 10[/tex].
- [tex]2p = 10d +10[/tex].
- [tex]p - 5 = 5d + 5[/tex]
The table of values is not given; so, I will answer the question with the following table of values of a linear function.
[tex]\left[\begin{array}{cccccc}d&1&2&3&4&5\\p&15&20&25&30&35\end{array}\right][/tex]
First, calculate the slope (m)
[tex]m = \frac{p_2 - p_1}{d_2 - d_1}[/tex]
So, we have:
[tex]m = \frac{20 - 15}{2 - 1}[/tex]
[tex]m = \frac{5}{1}[/tex]
[tex]m=5[/tex]
The equation is then calculated as:
[tex]p =m(d - d_1) + p_1[/tex]
This gives:
[tex]p =5(d - 1) + 15[/tex]
Open brackets
[tex]p =5d - 5 + 15[/tex]
[tex]p =5d + 10[/tex]
To get an equivalent expression, we must perform the same operation on both sides of the equation.
Multiply both sides of [tex]p =5d + 10[/tex] by 2
[tex]2 \times p =(5d + 10) \times 2[/tex]
[tex]2p = 10d +10[/tex]
Subtract 5 from both sides of [tex]p =5d + 10[/tex]
[tex]p - 5 = 5d + 10 - 5[/tex]
[tex]p - 5 = 5d + 5[/tex]
Hence, the equivalent expressions are:
- [tex]p =5d + 10[/tex].
- [tex]2p = 10d +10[/tex].
- [tex]p - 5 = 5d + 5[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/21213498
