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Graph the following inequality. -5x+3y > -15

Graph the following inequality. -5x+3y > -15

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Graphing Linear Inequalities In this lesson, we will learn how to graph the linear inequality given below: \[ -5x + 3y > -15 \] To graph this inequality, follow these steps: 1. **Rewrite the Inequality:** Convert the inequality to slope-intercept form, \( y = mx + b \), or an equivalent form if possible. Given the inequality: \[ -5x + 3y > -15 \] Isolate y: \[ 3y > 5x - 15 \] \[ y > \frac{5}{3}x - 5 \] 2. **Graph the Boundary Line:** Treat the inequality as an equation to draw its boundary: \[ y = \frac{5}{3}x - 5 \] Since the inequality is strictly greater than ( > ) and not greater than or equal to ( ≥ ), the boundary line should be drawn as a dashed line to indicate that points on the line are not included in the solution set. 3. **Shading the Solution Area:** Determine the region that satisfies the inequality. Since y is greater than the expression, shade the area above the dashed line. #### Graph Explanation: To aid comprehension, utilize graphing tools to visualize the inequality. Here is a sample graph for reference: - **X-Axis and Y-Axis:** The graph has a standard Cartesian coordinate system with x and y axes, each ranging from -10 to 10. - **Dashed line:** Represents the line \( y = \frac{5}{3}x - 5 \). - **Shaded Region:** The region above the dashed line, representing all (x, y) pairs that satisfy the inequality \( y > \frac{5}{3}x - 5 \). Click the graph to enlarge and examine the graph more closely. **Additional Tips:** - Always check your solution by picking a test point (not on the boundary line) to confirm the correct region is shaded. - Use graphing tools or software as needed to ensure accuracy in drawing and shading. **Interactive Graphing Tool:** Utilize the graphing tool provided. Click the graph, choose a tool from the palette, and follow the on-screen instructions to create your graph. This tool helps visualize and correctly plot inequalities, providing an enhanced learning experience. Date Added: 06/29
Transcribed Image Text:### Graphing Linear Inequalities In this lesson, we will learn how to graph the linear inequality given below: \[ -5x + 3y > -15 \] To graph this inequality, follow these steps: 1. **Rewrite the Inequality:** Convert the inequality to slope-intercept form, \( y = mx + b \), or an equivalent form if possible. Given the inequality: \[ -5x + 3y > -15 \] Isolate y: \[ 3y > 5x - 15 \] \[ y > \frac{5}{3}x - 5 \] 2. **Graph the Boundary Line:** Treat the inequality as an equation to draw its boundary: \[ y = \frac{5}{3}x - 5 \] Since the inequality is strictly greater than ( > ) and not greater than or equal to ( ≥ ), the boundary line should be drawn as a dashed line to indicate that points on the line are not included in the solution set. 3. **Shading the Solution Area:** Determine the region that satisfies the inequality. Since y is greater than the expression, shade the area above the dashed line. #### Graph Explanation: To aid comprehension, utilize graphing tools to visualize the inequality. Here is a sample graph for reference: - **X-Axis and Y-Axis:** The graph has a standard Cartesian coordinate system with x and y axes, each ranging from -10 to 10. - **Dashed line:** Represents the line \( y = \frac{5}{3}x - 5 \). - **Shaded Region:** The region above the dashed line, representing all (x, y) pairs that satisfy the inequality \( y > \frac{5}{3}x - 5 \). Click the graph to enlarge and examine the graph more closely. **Additional Tips:** - Always check your solution by picking a test point (not on the boundary line) to confirm the correct region is shaded. - Use graphing tools or software as needed to ensure accuracy in drawing and shading. **Interactive Graphing Tool:** Utilize the graphing tool provided. Click the graph, choose a tool from the palette, and follow the on-screen instructions to create your graph. This tool helps visualize and correctly plot inequalities, providing an enhanced learning experience. Date Added: 06/29
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