A hiker is descending a hill. The table represents the hiker's elevation in feet, y
, after x
 minutes.
 
Time (mins)	1
2
3
4
Elevation (ft)	180
160
140
120

Which equation represents the linear relationship between the x
-values and the y
-values in the table?
A.y=20+200x

B.y=20x−200

C.y=−20x−200

D.y=−20x+200



The problem presents a linear relationship between the hiker's time descending the hill (x, in minutes) and the elevation (y, in feet). We need to find the equation that represents this relationship.

### Step 1: Check the rate of change (slope).
The hiker's elevation decreases as time passes, so let's calculate the slope \( m \), which is the rate of change.

Using the formula for slope between two points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (1, 180) and (2, 160):
\[
m = \frac{160 - 180}{2 - 1} = \frac{-20}{1} = -20
\]
So, the slope \( m \) is \( -20 \).

### Step 2: Use the slope-intercept form of the equation of a line.
The equation of a line is:
\[
y = mx + b
\]
Where:
- \( m \) is the slope, which we found to be \( -20 \).
- \( b \) is the y-intercept, which we can find by using one of the points.

### Step 3: Find the y-intercept \( b \).
Using the point (1, 180) and the slope \( m = -20 \):
\[
y = mx + b
\]
\[
180 = -20(1) + b
\]
\[
180 = -20 + b
\]
\[
b = 200
\]

Thus, the equation is:
\[
y = -20x + 200
\]

### Conclusion:
The correct equation is:
\[
\boxed{D. \, y = -20x + 200}
\]

Would you like more details, or have any other questions?

### 5 Related Questions:
1. How do you determine the slope from a table of values?
2. How does a negative slope affect the relationship between the variables?
3. What does the y-intercept represent in this problem?
4. How would the equation change if the hiker were ascending the hill?
5. Can you graph the equation and interpret the slope visually?

### Tip:
When working with linear equations, always check if the change in y-values is consistent for equal changes in x-values to confirm linearity.

A hiker is descending a hill. The table represents the hiker's elevation in feet, y, after x minutes.

Time (mins): 1, 2, 3, 4
Elevation (ft): 180, 160, 140, 120

Which equation represents the linear relationship between the x-values and the y-values in the table?
A. y = 20 + 200x
B. y = 20x − 200
C. y = −20x − 200
D. y = −20x + 200

Discover how to determine the linear equation for a hiker's descent from a hill based on time and elevation data. Learn about slope calculation and slope-intercept form. This problem is suitable for students in Grades 6-8 and involves key algebraic concepts.

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