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To find an explicit formula that matches the line shown in the graph, we can determine the equation of the line by using two points given on the graph. 

### Step 1: Identify Points
The graph includes the points:
1. \((-3, 4)\)
2. \((4, 3)\)

### Step 2: Calculate the Slope
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points \((-3, 4)\) and \((4, 3)\):
\[
m = \frac{3 - 4}{4 - (-3)} = \frac{-1}{7} = -\frac{1}{7}
\]

### Step 3: Use the Point-Slope Form
The point-slope form of a line's equation is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((4, 3)\) and the slope \(m = -\frac{1}{7}\):
\[
y - 3 = -\frac{1}{7}(x - 4)
\]

### Step 4: Simplify to Slope-Intercept Form
Expanding the equation:
\[
y - 3 = -\frac{1}{7}x + \frac{4}{7}
\]
Add 3 to both sides to solve for \( y \):
\[
y = -\frac{1}{7}x + \frac{4}{7} + 3
\]
Convert 3 to a fraction with a denominator of 7:
\[
y = -\frac{1}{7}x + \frac{4}{7} + \frac{21}{7}
\]
\[
y = -\frac{1}{7}x + \frac{25}{7}
\]

### Final Answer
The explicit formula that matches the graph is:
\[
y = -\frac{1}{7}x + \frac{25}{7}
\]

Would you like further explanation on any of the steps?

### Additional Questions
1. How do you find the slope between any two points on a line?
2. What is the point-slope form of a line and how is it used?
3. How can you convert from point-slope form to slope-intercept form?
4. What does the slope represent in terms of the line's direction?
5. Why is it helpful to have an equation for a line when given a graph?

### Tip
When finding the slope, carefully check each coordinate to ensure accuracy, especially if dealing with negative values.

Use the graph to fill in an answer to the sentence below and find an explicit formula that matches the graph.

Learn how to determine the equation of a line from two given points on a graph. This problem walks through calculating the slope and using the point-slope form to derive an explicit formula for the line.

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