Question

Jamal is creating an input/output table for a linear function. Enter a number in each box to complete the table.

Question 1 Response area with 3 text input boxes
Input

Output

negative 6 negative 22
negative 4

negative 16

negative 1


5



32


Question 2
,begin emphasis,Part B,end emphasis,
Choose ,begin emphasis,all,end emphasis, linear functions with a slope that is greater than Jamal's linear function.

Question 2 Answer options with 6 options
A.
y equals 6

B.
y equals 5 x

C.
y equals negative 4 x

D.
y equals 4 x plus 3

E.
y equals x plus 10

F.
y equals 8-thirds x plus 4

Answer 1

To complete Jamal's input/output table for a linear function, we first need to deduce the linear equation based on the given points in the table.

From the data provided:

1. For **Input = -6**, **Output = -22**
2. For **Input = -4**, **Output = ?**
3. For **Input = -1**, **Output = 5**
4. For **Input = ?,** **Output = 32**

Let's start with the first two points.

We need to find the slope (m) using the formula:

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

Using the known points (-6, -22) and (-1, 5):

\[
m = \frac{5 - (-22)}{-1 - (-6)} = \frac{27}{5} = 5.4
\]

Now, we can use the slope-intercept form of a line, \(y = mx + b\), to find the y-intercept (b). We can use either point to find b. Let’s use (-6, -22):

\[
-22 = 5.4(-6) + b
\]
\[
-22 = -32.4 + b
\]
\[
b = -22 + 32.4 = 10.4
\]

Now we have the equation of the line:

\[
y = \frac{27}{5}x + 10.4
\]

Next, let’s fill in the missing outputs in the table:

For **Input = -4**:

\[
y = \frac{27}{5}(-4) + 10.4 = -21.6 + 10.4 = -11.2
\]

So, the output for Input = -4 is -11.2.

For **Input = -1**, we already have the output as 5 which is consistent with our equation.

Now, for the last row which needs an input for Output = 32:

\[
32 = \frac{27}{5}x + 10.4
\]
\[
32 - 10.4 = \frac{27}{5}x
\]
\[
21.6 = \frac{27}{5}x
\]
\[
x = \frac{21.6 \cdot 5}{27} = 4
\]

So the input for Output = 32 is 4.

Now, here is the completed table:

| Input | Output |
|-------|--------|
| -6 | -22 |
| -4 | -11.2 |
| -1 | 5 |
| 4 | 32 |

---

Now for Question 2, we are to choose all linear functions with a slope greater than Jamal's linear function slope, which we calculated as \(m = 5.4\).

Let’s evaluate the given options based on their slopes:

A. \(y = 6\) → slope = 0

B. \(y = 5x\) → slope = 5

C. \(y = -4x\) → slope = -4

D. \(y = 4x + 3\) → slope = 4

E. \(y = x + 10\) → slope = 1

F. \(y = \frac{8}{3}x + 4\) → slope = \(\frac{8}{3} \approx 2.67\)

The only functions with slopes greater than 5.4 are none from these options.

Therefore, **none of the choices (A, B, C, D, E, F)** have slopes greater than 5.4.

If you need further clarification or additional information, feel free to ask!