Question

Write a function rule for

X

Y

-4

0

-2

1

0

2

2

3

4

4

M = ___
B = ___
Function Rule: ____

Answer 1

To find the function rule for the data points given, we first note the pairs of \( (X, Y) \):

- \( (-4, 0) \)
- \( (-2, 1) \)
- \( (0, 2) \)
- \( (2, 3) \)
- \( (4, 4) \)

This indicates a linear relationship since \( Y \) increases as \( X \) increases.

We can determine the slope \( M \) (or gradient) of the line using the formula:
\[
M = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the points \( (0, 2) \) and \( (4, 4) \):
- \( y_1 = 2 \), \( x_1 = 0 \)
- \( y_2 = 4 \), \( x_2 = 4 \)

Plugging in these values into the slope formula:
\[
M = \frac{4 - 2}{4 - 0} = \frac{2}{4} = \frac{1}{2}
\]

Now, we can use one of the points to find the y-intercept \( B \). Let's use the point \( (0, 2) \), where \( X = 0 \) corresponds to \( Y = B \):
\[
B = 2
\]

Now we can write the function rule using these values:
\[
Y = MX + B
\]
Substituting in the values of \( M \) and \( B \):
\[
Y = \frac{1}{2}X + 2
\]

So, summarizing the results:
- \( M = \frac{1}{2} \)
- \( B = 2 \)
- Function Rule: \( Y = \frac{1}{2}X + 2 \)