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The graph shows the linear function \( g \) passing through the points \( (-8, 3) \) and \( (-3, -4.5) \). To determine the zero of the function, we need to find the x-intercept, which is the value of \( x \) when \( y = 0 \).

Let's start by finding the equation of the line in slope-intercept form \( y = mx + b \).

### Step 1: Calculate the slope \( m \)

The formula for slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Substituting the given points \( (-8, 3) \) and \( (-3, -4.5) \):

\[
m = \frac{-4.5 - 3}{-3 - (-8)} = \frac{-7.5}{5} = -1.5
\]

So, the slope \( m = -1.5 \).

### Step 2: Use point-slope form to find the equation of the line

Now, using the point-slope form of the equation of a line, \( y - y_1 = m(x - x_1) \), we can substitute one of the points, say \( (-8, 3) \), and the slope \( m = -1.5 \):

\[
y - 3 = -1.5(x - (-8)) = -1.5(x + 8)
\]

Simplifying:

\[
y - 3 = -1.5x - 12
\]
\[
y = -1.5x - 9
\]

### Step 3: Find the zero of the function

To find the zero, set \( y = 0 \) and solve for \( x \):

\[
0 = -1.5x - 9
\]

Add 9 to both sides:

\[
1.5x = -9
\]

Now, divide by 1.5:

\[
x = -6
\]

Thus, the zero of the function \( g \) is \( x = -6 \).

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Do you need further clarification or more details?

Here are 5 related questions to explore further:
1. How can we verify that the equation of the line is correct using both points?
2. What is the significance of the slope in a linear function?
3. How do we interpret the y-intercept of the function?
4. Can you find the zero of a quadratic function using a similar method?
5. What is the connection between the slope and the steepness of a line?

**Tip**: When calculating the slope, always double-check the signs of your coordinates to ensure accuracy!

Learn how to find the zero of the linear function g by calculating the slope and equation of the line passing through points (-8, 3) and (-3, -4.5). The step-by-step solution includes finding the x-intercept by solving for when y equals 0.

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