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To find the *x*-intercept of the graph of the linear function shown in the table, we first need to establish the equation of the line by determining the slope and y-intercept, then solve for the *x*-intercept.

### Step 1: Find the slope (m)
The slope \( m \) of a line is given by:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]
We can take any two points from the table. Let's use the points (-3, 18) and (-2, 16):
\[
m = \frac{{16 - 18}}{{-2 - (-3)}} = \frac{{-2}}{{1}} = -2
\]
Thus, the slope is \( m = -2 \).

### Step 2: Use the point-slope form to find the equation of the line
We can now use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = -2 \) and the point (-3, 18):
\[
y - 18 = -2(x + 3)
\]
Simplifying:
\[
y - 18 = -2x - 6
\]
\[
y = -2x + 12
\]
So the equation of the line is \( y = -2x + 12 \).

### Step 3: Find the *x*-intercept
The *x*-intercept occurs when \( y = 0 \). Substituting \( y = 0 \) into the equation:
\[
0 = -2x + 12
\]
Solving for \( x \):
\[
2x = 12
\]
\[
x = 6
\]

Thus, the *x*-intercept is \( x = 6 \).

The correct answer is 6.

Would you like further explanation or details?

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Here are five related questions to expand your understanding:
1. What is the significance of the slope in a linear function?
2. How can you quickly identify the *y*-intercept from the equation of a line?
3. How do changes in slope affect the steepness of a line?
4. What are the differences between *x*-intercepts and *y*-intercepts?
5. How would you find the *y*-intercept using the points in the table?

**Tip:** Remember, the *x*-intercept is where the line crosses the x-axis, and at this point, \( y = 0 \).

What is the x-intercept of the graph of this function?

Learn how to find the x-intercept of a linear function by analyzing pairs of values and determining the equation of the line. This problem involves calculating the slope, using point-slope form, and finding where y equals zero. Suitable for students in Grades 8-10.

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