Question

identify the x and y intercept from each table.
x
5,4,3,2,1

y
0,3,6,9,12

Answer 1

what would the slope =

Answer 2

To identify the x and y intercepts from the given data, we will analyze the values provided in the tables.

### Given Data:
- \( x: 5, 4, 3, 2, 1 \)
- \( y: 0, 3, 6, 9, 12 \)

### Finding the Intercepts:

1. **Y-Intercept**:
The y-intercept occurs where \( x = 0 \). Since \( x = 0 \) is not present in the table, we cannot directly find the y-intercept from the given values. However, with the data provided, it appears that as \( x \) decreases, \( y \) increases, suggesting a linear relationship. To find the y-intercept, we can use the pattern of the line formed by the given points and determine where it would cross the y-axis.

Observing the values, we see that subtracting \( y \) from the previous \( y \) values gives a constant change:
- \( y(5) = 0 \)
- \( y(4) = 3 \) (change of +3)
- \( y(3) = 6 \) (change of +3)
- \( y(2) = 9 \) (change of +3)
- \( y(1) = 12 \) (change of +3)

This indicates a slope of \( -3 \) (since \( y \) increases by 3 as \( x \) decreases by 1).
Extrapolating down to \( x = 0 \):
- When \( x = 0 \), \( y = 12 + 3 = 15 \).

Therefore, the y-intercept is \( (0, 15) \).

2. **X-Intercept**:
The x-intercept occurs where \( y = 0 \). From the data provided:
- The only time \( y = 0 \) is when \( x = 5 \).

Thus, the x-intercept is \( (5, 0) \).

### Summary of Intercepts:
- **X-Intercept**: \( (5, 0) \)
- **Y-Intercept**: \( (0, 15) \)

Answer 3

To calculate the slope of the line formed by the points in your data table, you can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the given data:
- The points are \((5, 0)\), \((4, 3)\), \((3, 6)\), \((2, 9)\), and \((1, 12)\).

Let's calculate the slope between the first two points, \((5, 0)\) and \((4, 3)\).

Using:
- \((x_1, y_1) = (5, 0)\)
- \((x_2, y_2) = (4, 3)\)

The slope calculation is:

\[
m = \frac{3 - 0}{4 - 5} = \frac{3}{-1} = -3
\]

### Slope Calculation Between Different Points
You can verify that the slope remains constant by calculating between other pairs of points as well:

1. For points \((4, 3)\) and \((3, 6)\):
\[
m = \frac{6 - 3}{3 - 4} = \frac{3}{-1} = -3
\]

2. For points \((3, 6)\) and \((2, 9)\):
\[
m = \frac{9 - 6}{2 - 3} = \frac{3}{-1} = -3
\]

3. For points \((2, 9)\) and \((1, 12)\):
\[
m = \frac{12 - 9}{1 - 2} = \frac{3}{-1} = -3
\]

### Conclusion
The slope \( m \) of the line formed by the given points is \(-3\). This indicates that for every 1 unit increase in \( x \), \( y \) decreases by 3 units (hence the negative slope).