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Which point is in the solution set for question 9? y≤-2x+5 3 y²-x-2

Which point is in the solution set for question 9? y≤-2x+5 3 y²-x-2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(0,0)

(4,1)

(2,4)

(-2,-3)

**Which point is in the solution set for question 9?** 1. \( y \leq -2x + 5 \) 2. \( y \geq \frac{3}{2}x - 2 \) *Explanation:* We are tasked with finding a point that satisfies both inequalities. This requires identifying a coordinate \((x, y)\) such that it lies within the shaded region where these two lines intersect on a graph. 1. **First Inequality:** - The inequality \( y \leq -2x + 5 \) represents a line with a slope of \(-2\) and a y-intercept of \(5\). The region of interest is below this line. 2. **Second Inequality:** - The inequality \( y \geq \frac{3}{2}x - 2 \) represents a line with a slope of \(\frac{3}{2}\) and a y-intercept of \(-2\). The region of interest is above this line. For a point to be in the solution set, it must satisfy both conditions, lying below the first line and above the second line. Visual graphing tools or manual calculation would help in identifying such a point.
Transcribed Image Text:**Which point is in the solution set for question 9?** 1. \( y \leq -2x + 5 \) 2. \( y \geq \frac{3}{2}x - 2 \) *Explanation:* We are tasked with finding a point that satisfies both inequalities. This requires identifying a coordinate \((x, y)\) such that it lies within the shaded region where these two lines intersect on a graph. 1. **First Inequality:** - The inequality \( y \leq -2x + 5 \) represents a line with a slope of \(-2\) and a y-intercept of \(5\). The region of interest is below this line. 2. **Second Inequality:** - The inequality \( y \geq \frac{3}{2}x - 2 \) represents a line with a slope of \(\frac{3}{2}\) and a y-intercept of \(-2\). The region of interest is above this line. For a point to be in the solution set, it must satisfy both conditions, lying below the first line and above the second line. Visual graphing tools or manual calculation would help in identifying such a point.
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