Question

Using the table bellow fill in the blanks

X 1 2 3 4
Y -12 -15 -18 -21

The slope function is *blank 1*

The y-intercept of the function is *blank 2* *blank 3

Options for blank 1

A -1/3
B 3
C -3
D 1/3

Options blank 2

A 1
B 0
C 4
D 2
E 3

Options for blank 3

A -18
B -21
C -9
D -15
E -12

Answer 1

To fill in the blanks, we first need to analyze the given data points (X, Y):

- When \(X = 1\), \(Y = -12\)
- When \(X = 2\), \(Y = -15\)
- When \(X = 3\), \(Y = -18\)
- When \(X = 4\), \(Y = -21\)

### To calculate the slope (Blank 1):
The slope \(m\) can be calculated using the formula:
\[
m = \frac{Y_2 - Y_1}{X_2 - X_1}
\]
Using two points, for instance, (1, -12) and (2, -15):
\[
m = \frac{-15 - (-12)}{2 - 1} = \frac{-15 + 12}{1} = \frac{-3}{1} = -3
\]

So, the slope function is **C -3**.

### To calculate the y-intercept (Blanks 2 and 3):
Using the slope-intercept form of the line, \(Y = mX + b\), we can rearrange it to find \(b\) (the y-intercept) using one of the points. Let's use (1, -12):
\[
-12 = -3(1) + b
\]
\[
-12 = -3 + b
\]
\[
b = -12 + 3 = -9
\]

This means the y-intercept is \(b = -9\).

So, we need to choose options for Blank 2 and Blank 3. Since we have established that the y-intercept is \(y = -9\):

- Blank 2 can be inferred as **B 0** (for the y-intercept in the context of graphing being a point on the Y-axis).
- Blank 3 can be inferred as **C -9** (the actual value of the y-intercept).

Putting it all together:
- Blank 1: **C -3**
- Blank 2: **B 0**
- Blank 3: **C -9**