Find the coordinates of points P and Q in the figure below. (?, ?) Q = (?, ?) P = y = √x P 4 9 X Write an equation for the line connecting the two points. NOTE: Write the answer as an equation with using exact values.
Find the coordinates of points P and Q in the figure below. (?, ?) Q = (?, ?) P = y = √x P 4 9 X Write an equation for the line connecting the two points. NOTE: Write the answer as an equation with using exact values.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Find the coordinates of points \( P \) and \( Q \) in the figure below.**
The graph shows the function \( y = \sqrt{x} \). Two points, \( P \) and \( Q \), are marked on this curve.
- Point \( P \) has an x-coordinate of 4.
- Point \( Q \) has an x-coordinate of 9.
Evaluate the function \( y = \sqrt{x} \) to find the y-coordinates for both points:
- For point \( P \): \( y = \sqrt{4} = 2 \)
- For point \( Q \): \( y = \sqrt{9} = 3 \)
Therefore, the coordinates are:
\[ P = (4, 2) \]
\[ Q = (9, 3) \]
**Write an equation for the line connecting the two points.**
To find the equation of the line passing through points \( P \) and \( Q \), use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 2}{9 - 4} = \frac{1}{5} \]
Using the point-slope form \( y - y_1 = m(x - x_1) \):
- Choose point \( P = (4, 2) \):
The equation becomes:
\[ y - 2 = \frac{1}{5}(x - 4) \]
Simplifying:
\[ y = \frac{1}{5}x + \frac{6}{5} \]
**NOTE:** Write the answer as an equation using exact values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92ab3c20-a3cd-4c1e-8775-52ac5ed4d4cf%2F17dace08-5b61-4946-8b4d-de88ff69420d%2Foxtcuu_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the coordinates of points \( P \) and \( Q \) in the figure below.**
The graph shows the function \( y = \sqrt{x} \). Two points, \( P \) and \( Q \), are marked on this curve.
- Point \( P \) has an x-coordinate of 4.
- Point \( Q \) has an x-coordinate of 9.
Evaluate the function \( y = \sqrt{x} \) to find the y-coordinates for both points:
- For point \( P \): \( y = \sqrt{4} = 2 \)
- For point \( Q \): \( y = \sqrt{9} = 3 \)
Therefore, the coordinates are:
\[ P = (4, 2) \]
\[ Q = (9, 3) \]
**Write an equation for the line connecting the two points.**
To find the equation of the line passing through points \( P \) and \( Q \), use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 2}{9 - 4} = \frac{1}{5} \]
Using the point-slope form \( y - y_1 = m(x - x_1) \):
- Choose point \( P = (4, 2) \):
The equation becomes:
\[ y - 2 = \frac{1}{5}(x - 4) \]
Simplifying:
\[ y = \frac{1}{5}x + \frac{6}{5} \]
**NOTE:** Write the answer as an equation using exact values.
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