The graph in the image shows a scatter plot with three visible points: $(1, 5)$, $(4, 1)$, and $(7, -3)$. The points seem to follow a linear pattern. To find the explicit formula that matches the graph, let's determine the equation of the line passing through these points.

Step 1: Find the slope of the line

The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(1, 5)$ and $(4, 1)$: $m = \frac{1 - 5}{4 - 1} = \frac{-4}{3}$

Step 2: Use the point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using the point $(1, 5)$ and the slope $m = -\frac{4}{3}$: $y - 5 = -\frac{4}{3}(x - 1)$

Step 3: Simplify to slope-intercept form

Expand and simplify the equation: $y - 5 = -\frac{4}{3}x + \frac{4}{3}$ $y = -\frac{4}{3}x + \frac{4}{3} + 5$ $y = -\frac{4}{3}x + \frac{4}{3} + \frac{15}{3}$ $y = -\frac{4}{3}x + \frac{19}{3}$

Thus, the equation of the line that matches the graph is: $y = -\frac{4}{3}x + \frac{19}{3}$

Would you like more details on this solution, or do you have any specific questions?

5 Related Questions:

1. How can you find the slope if only two points are given?
2. What is the significance of the y-intercept in a linear equation?
3. How do you convert a linear equation from point-slope form to slope-intercept form?
4. Can you determine the type of sequence from the points on a graph?
5. How would the equation change if the points followed a quadratic pattern?

Tip: When working with linear equations, always check multiple points on the graph to confirm the pattern.