Question

Complete the table for the function y=6x.
x y
–1
0
1
2
Now, graph the function.

Answer 1

numbers on x axis and y axis only go up to 8 or -8

Answer 2

To complete the table for the function \( y = 6x \), we can substitute the given values of \( x \) into the equation.

1. For \( x = -1 \):
\[
y = 6(-1) = -6
\]

2. For \( x = 0 \):
\[
y = 6(0) = 0
\]

3. For \( x = 1 \):
\[
y = 6(1) = 6
\]

4. For \( x = 2 \):
\[
y = 6(2) = 12
\]

Now, the completed table is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & -6 \\
0 & 0 \\
1 & 6 \\
2 & 12 \\
\hline
\end{array}
\]

Next, let's summarize the points to graph:
- Point 1: \((-1, -6)\)
- Point 2: \((0, 0)\)
- Point 3: \((1, 6)\)
- Point 4: \((2, 12)\)

### Graph of the function \( y = 6x \)

To graph the function, you would plot these points on a coordinate grid:

1. Plot the point \((-1, -6)\).
2. Plot the point \((0, 0)\).
3. Plot the point \((1, 6)\).
4. Plot the point \((2, 12)\).

Then, draw a straight line through these points, representing the linear equation \( y = 6x \). The slope is 6, indicating that for every unit increase in \( x \), \( y \) increases by 6 units.

### Note:
I'm unable to create visual representations directly, but you can easily graph this using graphing software or graph paper. Draw the x-axis and y-axis, plot the points based on the completed table, and connect them to show the straight line of the function.

Answer 3

Given that the x-axis and y-axis only go up to 8 or -8, we can still plot the points of the function \( y = 6x \) that were calculated earlier, while noting any values that exceed the axis limits.

### Key Points to Plot
- \((-1, -6)\) is within the limits.
- \((0, 0)\) is within the limits.
- \((1, 6)\) is within the limits.
- \((2, 12)\) exceeds the y-axis limit of 8.

### Summary of Points to Plot
1. **\((-1, -6)\)** - This point is plotted on the graph.
2. **\((0, 0)\)** - This point is plotted at the origin.
3. **\((1, 6)\)** - This point is plotted above the x-axis.
4. **\((2, 12)\)** - This point cannot fully be plotted because the y-value (12) exceeds 8. However, you can plot a point at \((2, 8)\) to indicate that the function continues beyond the limit.

### Steps to Graph:
1. Draw the x-axis and y-axis. Label the axes from -8 to 8.
2. Mark the points:
- For \((-1, -6)\), find -1 on the x-axis and go down to -6 on the y-axis.
- For \((0, 0)\), find the origin where x and y are both 0.
- For \((1, 6)\), go to 1 on the x-axis and up to 6 on the y-axis.
- For \((2, 8)\), go to 2 on the x-axis and up to 8 on the y-axis to show where the line extends.
3. Connect the points with a straight line, showing the linear relationship of the function. The line should continue beyond the point \((2, 8)\) to reflect that it will keep increasing as \( x \) increases.

### Note:
The graph illustrates a linear function with a positive slope. Every point from the straight line shows the calculated values of \( y \) based on \( y = 6x \), but the line will visually indicate that the function continues beyond the plotted points.