To find the equation of the linear function represented by the points (4, 4) and (-4, -2), we first need to determine the slope (m) of the line.
The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's assign the points as follows:
- Point 1: \( (4, 4) \) \( (x_1, y_1) \)
- Point 2: \( (-4, -2) \) \( (x_2, y_2) \)
Now applying the slope formula:
\[ m = \frac{-2 - 4}{-4 - 4} = \frac{-6}{-8} = \frac{3}{4} \]
So the slope \( m = \frac{3}{4} \).
Next, we can use the point-slope form of a line to find the equation of the line. The point-slope form is:
\[ y - y_1 = m(x - x_1) \]
Using the point (4, 4):
\[ y - 4 = \frac{3}{4}(x - 4) \]
Now, we will distribute and rearrange to find the slope-intercept form (y = mx + b):
\[ y - 4 = \frac{3}{4}x - 3 \]
Adding 4 to both sides:
\[ y = \frac{3}{4}x + 1 \]
Thus, the equation of the line that best represents the graph is:
\[ y = \frac{3}{4}x + 1 \]