Question

Write a function rule for

X

Y

-2

0

-1

2

0

4

1

6

2

8

M = ___
B = ___
Function Rule: ____

Answer 1

To determine the function rule from the given points of \(X\) and \(Y\), we first need to identify the values of \(M\) (slope) and \(B\) (y-intercept).

Given the points:

- (-2, 0)
- (-1, 2)
- (0, 4)
- (1, 6)
- (2, 8)

Let's first find the slope \(M\). The slope \(M\) can be calculated using the formula:

\[
M = \frac{\text{change in } Y}{\text{change in } X} = \frac{Y_2 - Y_1}{X_2 - X_1}
\]

Choosing the points (0, 4) and (2, 8):

\[
M = \frac{8 - 4}{2 - 0} = \frac{4}{2} = 2
\]

Now that we have the slope \(M = 2\), we can find the y-intercept \(B\) by substituting one of the points into the equation \(Y = MX + B\).

Using the point (0, 4):

\[
4 = 2(0) + B \implies B = 4
\]

Thus, the values are:

\[
M = 2, \quad B = 4
\]

Finally, the function rule is:

\[
Y = 2X + 4
\]

To summarize:

- \(M = 2\)
- \(B = 4\)
- Function Rule: \(Y = 2X + 4\)