Question

The points given in each table lie on lines. Which table, when graphed, would show a negative slope? Multiple choice question. A) x −13 −9 −5 −1 y −4 −2 0 2 B) x −2 3 8 13 y −2 −1 0 1 C) x −1 1 3 5 y −2 0 2 4 D) x 3 5 6 8 y 8 0 −4 −12

Answer 1

Table D, which has the points (3, 8), (5, 0), (6, -4), and (8, -12), represents a straight line with a negative slope, as y decreases while x increases.

Step-by-step explanation:

To determine which table has points that would yield a negative slope when graphed, we should look at the change in y-values relative to the change in x-values. A negative slope is characterized by a decrease in the y-value as the x-value increases. By examining the choices:

• A) The change from (−13,−4) to (−1,2) shows an increase in both x and y, indicating a positive slope.
• B) Similar to A, the x and y values both increase, suggesting a positive slope.
• C) Here, as x increases, y increases consistently, which also indicates a positive slope.
• D) Looking at option D, as x increases from 3 to 8, y decreases from 8 to −12, which meets the criteria of a negative relationship between x and y. This implies that the line would fall from left to right on a graph, and thus has a negative slope.

Therefore, table D represents a straight line with negative slope when graphed.

Answer 2

Table D

Step-by-step explanation:

To determine which table shows a negative slope, we need to identify which table has points that, when plotted on a graph, decrease from left to right.

Let's start by plotting the points in Table A on a graph:

y

|

| o

| o

| o

| o

|___________________________

x

As we can see, the points in Table A form a line that increases from left to right. So Table A does not have a negative slope.

Next, let's plot the points in Table B:

y

|

| o

| o

| o

| o

|___________________________

x

The points in Table B form a line that increases from left to right as well. So Table B does not have a negative slope.

Now, let's plot the points in Table C:

y

|

| o

| o

| o

| o

|___________________________

x

The points in Table C form a line that increases from left to right, so Table C does not have a negative slope either.

Finally, let's plot the points in Table D:

y

|

| o

| o

| o

| o

|___________________________

x

The points in Table D form a line that decreases from left to right, so Table D has a negative slope.

Therefore, the correct answer is D.