Certainly! Let's tackle each part of this question step by step.
### Part (a)
To write an equation in the form [tex]\( y = mx + b \)[/tex] for this cell phone plan, we need to identify what [tex]\( m \)[/tex] and [tex]\( b \)[/tex] represent.
- [tex]\( m \)[/tex] represents the cost per month. Here, the cost is [tex]$40 per month.
- \( b \) represents the one-time activation fee. This fee is $[/tex]32.
So, the equation in slope-intercept form [tex]\( y = mx + b \)[/tex] for this situation is:
[tex]\[ y = 40x + 32 \][/tex]
### Part (b)
Next, we need to find and interpret the ordered pair associated with the equation for [tex]\( x = 7 \)[/tex].
- Substitute [tex]\( x = 7 \)[/tex] into the equation [tex]\( y = 40x + 32 \)[/tex]:
[tex]\[ y = 40(7) + 32 \][/tex]
[tex]\[ y = 280 + 32 \][/tex]
[tex]\[ y = 312 \][/tex]
Therefore, the ordered pair is [tex]\( (7, 312) \)[/tex].
Interpretation of the ordered pair: When [tex]\( x = 7 \)[/tex], it represents the cost after 7 months. So, after 7 months, the total cost of the cell phone plan is [tex]$312.
### Part (c)
Finally, we calculate the total cost over a two-year contract. Since there are 12 months in a year, a two-year contract means \( 24 \) months.
- Substitute \( x = 24 \) into the equation \( y = 40x + 32 \):
\[ y = 40(24) + 32 \]
\[ y = 960 + 32 \]
\[ y = 992 \]
Total cost: Over a two-year contract (24 months), the total cost of this plan is $[/tex]992.
To summarize:
(a) The equation is [tex]\( y = 40x + 32 \)[/tex].
(b) The ordered pair for [tex]\( x = 7 \)[/tex] is [tex]\( (7, 312) \)[/tex], which means after 7 months, the total cost is [tex]$312.
(c) Over a two-year contract, the cost will be $[/tex]992.
