https://file.aiquickdraw.com/mathbot/file/1726291018339z6k8dciv.jpg

Let's work through the problem step by step using the information from the graph.

### (a) Find the slope of the pictured secant line.
The slope of a secant line between two points on a curve is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
From the graph, we need to identify the coordinates of the two points where the secant line intersects the curve. The two points on the curve appear to be approximately:

- \( P_1(-1, 1) \)
- \( P_2(3, 5) \)

Now, applying the slope formula:

\[
m = \frac{5 - 1}{3 - (-1)} = \frac{4}{4} = 1
\]

So, the slope of the secant line is \( m = 1 \).

---

### (b) Write the equation of the secant line (use function notation).
The equation of a line is generally given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope.

We already calculated \( m = 1 \). Let's use the point \( P_1(-1, 1) \) to find the equation:
\[
y - 1 = 1(x - (-1))
\]
Simplifying:
\[
y - 1 = x + 1
\]
\[
y = x + 2
\]

Thus, the equation of the secant line is:
\[
y = x + 2
\]

Alternatively, using function notation:
\[
f(x) = x + 2
\]

---

Do you want more details or have any questions?

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### 5 Related Questions:
1. What is the difference between a secant line and a tangent line?
2. How do you find the slope of a tangent line to a curve at a specific point?
3. Can a secant line have the same slope as the tangent line at one point? If so, when?
4. What are other ways to find the equation of a line given two points?
5. How would you apply the concept of secant lines in calculus, especially when dealing with limits?

### Tip:
When finding the slope of a secant line, it helps to clearly identify the coordinates of the points and double-check them to ensure accuracy in calculations.

Find the slope of the secant line and write the equation of the secant line using function notation.

Learn how to find the slope of a secant line and write its equation using function notation. This problem covers the key algebraic concepts of slope and point-slope form, suitable for students in Grades 8-10.

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