https://file.aiquickdraw.com/mathbot/file/1726398484325ukivepvr.jpg

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.

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

Learn how to find the equation of a line using a graph. This example shows how to apply the slope formula and convert a point-slope equation to slope-intercept form. Explore key algebraic concepts suitable for high school students.

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