The table in the image represents the values of a linear function. We are tasked with finding the x- and y-intercepts of the function based on the data provided.

The x-values and corresponding y-values are:

• $x = -3$, $F(x) = 10$
• $x = -1$, $F(x) = -3$
• $x = 1$, $F(x) = -2$
• $x = 3$, $F(x) = 2$

To find the x- and y-intercepts, we first need to determine the equation of the line that fits these points.

Steps:

1. Find the slope of the line (m): The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using two points from the table, for example, $(-3, 10)$ and $(-1, -3)$: $m = \frac{-3 - 10}{-1 - (-3)} = \frac{-13}{2} = -\frac{13}{2}$

2. Find the equation of the line: Using the point-slope form of the equation of a line: $y - y_1 = m(x - x_1)$ Using the point $(-3, 10)$ and the slope $m = -\frac{13}{2}$: $y - 10 = -\frac{13}{2}(x + 3)$ Simplifying this equation will give the equation of the line.

3. Find the y-intercept (b): Set $x = 0$ and solve for $y$. This will give the y-intercept.

4. Find the x-intercept: Set $y = 0$ and solve for $x$. This will give the x-intercept.

Let's proceed with the calculations to determine the intercepts.

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