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Let's find the equation of the line that passes through the points \((5.7, -3)\) and \((8.7, 9.4)\) in slope-intercept form, \(y = mx + b\).

### Step 1: Find the slope (m)
The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points \((5.7, -3)\) and \((8.7, 9.4)\):

\[
m = \frac{9.4 - (-3)}{8.7 - 5.7} = \frac{9.4 + 3}{8.7 - 5.7} = \frac{12.4}{3} = 4.13
\]

### Step 2: Use the slope-intercept form
We now use the slope-intercept form \(y = mx + b\). To find the y-intercept \(b\), substitute one of the points and the slope into the equation. Let's use the point \((5.7, -3)\):

\[
y = mx + b
\]

\[
-3 = 4.13(5.7) + b
\]

Now, solve for \(b\):

\[
-3 = 23.541 + b
\]

\[
b = -3 - 23.541 = -26.541
\]

So the equation of the line is approximately:

\[
y = 4.13x - 26.54
\]

### Final Answer:
The closest option to this result is:

\[
\boxed{D. \ f(x) = 4.13x - 26.560}
\]

Would you like more details or have any questions?

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Here are 5 related questions you might find useful:
1. How can I derive the slope formula from the equation of a line?
2. What is the difference between slope-intercept form and point-slope form?
3. How do you graph a line given its equation in slope-intercept form?
4. What happens if two points have the same x-value or y-value when calculating the slope?
5. How does the slope affect the steepness and direction of a line?

**Tip:** Always round your intermediate values carefully to avoid significant rounding errors in the final result!

Find an equation of the line containing the given pair of points (5.7, -3) and (8.7, 9.4). Write your final answer as a linear function in slope-intercept form.

Learn how to find the equation of a line passing through the points (5.7, -3) and (8.7, 9.4). This problem uses the slope formula and slope-intercept form to derive the linear function. Suitable for students in Grades 8-10.

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