inital value and y intercept of (-3,4), (0,3),(3,2), (6,1)

Answer 1

To find the initial value and y-intercept of the given points \((-3, 4)\), \((0, 3)\), \((3, 2)\), and \((6, 1)\), we first need to understand what the y-intercept means. The y-intercept is the point where the line crosses the y-axis, which occurs when \(x = 0\).

From the points provided:

• The point \((0, 3)\) gives us the y-intercept directly as \(3\).

Thus, the y-intercept is \(3\).

Now, regarding the initial value, this term often refers to the value of a function at \(x = 0\) as well, which is also the y-intercept in linear functions.

Summary:

• y-intercept: 3
• Initial value at \(x = 0\): 3

If you need a linear equation that connects these points or if you need further analysis or extrapolation, please let me know!

Answer 2

initial value and rate of change

Answer 3

To find the initial value and the rate of change based on the points you provided \((-3, 4)\), \((0, 3)\), \((3, 2)\), and \((6, 1)\), we can represent the relationship between the values with a linear equation of the form \(y = mx + b\), where \(m\) is the rate of change (slope) and \(b\) is the y-intercept (initial value when \(x = 0\)).

Finding the Initial Value:

As previously mentioned, the y-intercept (initial value) from the point \((0, 3)\) is:

• Initial Value: \(b = 3\)

Finding the Rate of Change:

To calculate the rate of change (slope \(m\)), we can pick two points from the given data. The formula to find the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Let's use the points \((0, 3)\) and \((6, 1)\):

• \((x_1, y_1) = (0, 3)\)
• \((x_2, y_2) = (6, 1)\)

Calculating the slope:

\[ m = \frac{1 - 3}{6 - 0} = \frac{-2}{6} = -\frac{1}{3} \]

Summary:

• Initial Value: 3
• Rate of Change: \(-\frac{1}{3}\)

This means that for every unit increase in \(x\), the value of \(y\) decreases by \(\frac{1}{3}\).

Answer 4

A coordinate plane shows quadrant 4 with the x-axis, labeled as minutes, ranging from 0 to 6 in increments of 1 and y-axis, labeled as elevation in feet, ranging from 0 to negative 110 in decrements of 10. A ray with arrow at the bottom end points downward from the origin. The coordinates that it passes through are left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma negative 60 right parenthesis, and left parenthesis 5 comma negative 100 right parenthesis. The graph shows the elevation of a deep-sea diver in relation to minutes passed. Using any two points on the graph, what is the rate of change in the diver’s elevation?

Answer 5

To find the rate of change in the diver's elevation, we can use the formula for the slope (\(m\)) between any two points on the graph. The points you've provided are:

1. \((3, -60)\) - at 3 minutes, the elevation is -60 feet.
2. \((5, -100)\) - at 5 minutes, the elevation is -100 feet.

Using the formula for the slope:

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

Let's assign the points:

• Point 1: \((x_1, y_1) = (3, -60)\)
• Point 2: \((x_2, y_2) = (5, -100)\)

Now plug in the values:

\[ m = \frac{-100 - (-60)}{5 - 3} = \frac{-100 + 60}{5 - 3} = \frac{-40}{2} = -20 \]

Conclusion

The rate of change in the diver's elevation is \(-20\) feet per minute. This means that for every minute that passes, the diver's elevation decreases by 20 feet.