Question
In the table, x represents how many years Ms. Wilson has owned her necklace, and y represents the value of the necklace
Years, x Value in Dollars, y
0 $1,000
2 $1,750
4 $2,500
8 $4,000
(3 points)
The slope of the function is
because as the time Ms. Wilson has owned her necklace
, the value in dollars
.
Years, x Value in Dollars, y
0 $1,000
2 $1,750
4 $2,500
8 $4,000
(3 points)
The slope of the function is
because as the time Ms. Wilson has owned her necklace
, the value in dollars
.
Answers
Answered by
GPT-4o mini
To find the slope of the function represented by the data in the table, we need to calculate the change in the value of the necklace (y) per change in years (x).
We'll calculate the slope (m) between some of the points. Let's look at the points (0, 1000) and (2, 1750):
1. Change in value (Δy) = 1750 - 1000 = 750
2. Change in years (Δx) = 2 - 0 = 2
The slope between these two points is:
\[ m = \frac{Δy}{Δx} = \frac{750}{2} = 375 \]
We can similarly calculate the slope for other pairs of points to confirm the consistency:
For (2, 1750) and (4, 2500):
1. Change in value (Δy) = 2500 - 1750 = 750
2. Change in years (Δx) = 4 - 2 = 2
\[ m = \frac{750}{2} = 375 \]
For (4, 2500) and (8, 4000):
1. Change in value (Δy) = 4000 - 2500 = 1500
2. Change in years (Δx) = 8 - 4 = 4
\[ m = \frac{1500}{4} = 375 \]
The slope is consistent between the intervals calculated, confirming the relationship.
Thus, the slope of the function is **375** because as the time Ms. Wilson has owned her necklace **increases**, the value in dollars **increases at a rate of $375 per year**.
We'll calculate the slope (m) between some of the points. Let's look at the points (0, 1000) and (2, 1750):
1. Change in value (Δy) = 1750 - 1000 = 750
2. Change in years (Δx) = 2 - 0 = 2
The slope between these two points is:
\[ m = \frac{Δy}{Δx} = \frac{750}{2} = 375 \]
We can similarly calculate the slope for other pairs of points to confirm the consistency:
For (2, 1750) and (4, 2500):
1. Change in value (Δy) = 2500 - 1750 = 750
2. Change in years (Δx) = 4 - 2 = 2
\[ m = \frac{750}{2} = 375 \]
For (4, 2500) and (8, 4000):
1. Change in value (Δy) = 4000 - 2500 = 1500
2. Change in years (Δx) = 8 - 4 = 4
\[ m = \frac{1500}{4} = 375 \]
The slope is consistent between the intervals calculated, confirming the relationship.
Thus, the slope of the function is **375** because as the time Ms. Wilson has owned her necklace **increases**, the value in dollars **increases at a rate of $375 per year**.