Let f(x) = 2.6x² :3 and 2 = x1 = y = 6.3x. Find the equation of the secant line on the graph of f(x) between 9. Write your answer in mx + b format.
Let f(x) = 2.6x² :3 and 2 = x1 = y = 6.3x. Find the equation of the secant line on the graph of f(x) between 9. Write your answer in mx + b format.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.8: Interpreting Graphs Of Functions
Problem 1GP
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Question
![**Equation of the Secant Line**
Let \( f(x) = 2.6x^2 - 6.3x \). Find the equation of the secant line on the graph of \( f(x) \) between \( x_1 = 3 \) and \( x_2 = 9 \). Write your answer in \( mx + b \) format.
\( y = \) _____________
**Explanation:**
To find the equation of the secant line passing through the points \((x_1, f(x_1))\) and \((x_2, f(x_2))\), we follow these steps:
1. Calculate \( f(x) \) for both \( x_1 \) and \( x_2 \).
- For \( x_1 = 3 \):
\[
f(3) = 2.6(3)^2 - 6.3(3)
= 2.6(9) - 18.9
= 23.4 - 18.9
= 4.5
\]
- For \( x_2 = 9 \):
\[
f(9) = 2.6(9)^2 - 6.3(9)
= 2.6(81) - 56.7
= 210.6 - 56.7
= 153.9
\]
2. Find the slope (\(m\)) of the secant line:
\[
m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
= \frac{153.9 - 4.5}{9 - 3}
= \frac{149.4}{6}
= 24.9
\]
3. Use the slope-point form of a line equation, \( y - y_1 = m(x - x_1) \), with one of the points \((x_1, f(x_1))\):
- Using \((3, 4.5)\):
\[
y - 4.5 = 24.9(x - 3)
\]
Expanding and solving for \( y \):
\[
y = 24](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2133091-a753-411c-beef-444bf7f4574e%2Fb47aa6a4-58b0-4141-801d-c43fe4f40006%2F32n2pn7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation of the Secant Line**
Let \( f(x) = 2.6x^2 - 6.3x \). Find the equation of the secant line on the graph of \( f(x) \) between \( x_1 = 3 \) and \( x_2 = 9 \). Write your answer in \( mx + b \) format.
\( y = \) _____________
**Explanation:**
To find the equation of the secant line passing through the points \((x_1, f(x_1))\) and \((x_2, f(x_2))\), we follow these steps:
1. Calculate \( f(x) \) for both \( x_1 \) and \( x_2 \).
- For \( x_1 = 3 \):
\[
f(3) = 2.6(3)^2 - 6.3(3)
= 2.6(9) - 18.9
= 23.4 - 18.9
= 4.5
\]
- For \( x_2 = 9 \):
\[
f(9) = 2.6(9)^2 - 6.3(9)
= 2.6(81) - 56.7
= 210.6 - 56.7
= 153.9
\]
2. Find the slope (\(m\)) of the secant line:
\[
m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
= \frac{153.9 - 4.5}{9 - 3}
= \frac{149.4}{6}
= 24.9
\]
3. Use the slope-point form of a line equation, \( y - y_1 = m(x - x_1) \), with one of the points \((x_1, f(x_1))\):
- Using \((3, 4.5)\):
\[
y - 4.5 = 24.9(x - 3)
\]
Expanding and solving for \( y \):
\[
y = 24
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