Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine which statements are true about the linear inequality \( y > \frac{3}{4} x - 2 \), let's analyze it step-by-step:
1. The slope of the line is -2.
- This statement is false. The slope of the line is given by the coefficient of \( x \) in the inequality \( y = \frac{3}{4} x - 2 \). Therefore, the correct slope is \(\frac{3}{4}\), not -2.
2. The graph of \( y > \frac{3}{4} x - 2 \) is a dashed line.
- This statement is true. The inequality is a strict inequality (greater than) which means the line itself is not included in the solution set. Thus, it is represented by a dashed line.
3. The area below the line is shaded.
- This statement is false. For the inequality \( y > \frac{3}{4} x - 2 \), the region above the line is shaded because the inequality is "greater than" \( \frac{3}{4} x - 2 \).
4. One solution to the inequality is \((0,0)\).
- This statement is true. To check if \((0,0)\) is a solution, substitute \( x = 0 \) and \( y = 0 \) into the inequality:
[tex]\[ 0 > \frac{3}{4}(0) - 2 \implies 0 > -2 \][/tex]
Since this statement is true, \((0,0)\) is indeed a solution.
5. The graph intercepts the y-axis at \((0,-2)\).
- This statement is true. The y-axis intercept occurs where \( x = 0 \). Substituting \( x = 0 \) into the equation \( y = \frac{3}{4} x - 2 \) yields:
[tex]\[ y = \frac{3}{4}(0) - 2 = -2 \][/tex]
Therefore, the y-intercept is at \((0, -2)\).
Based on this analysis, the three correct options are:
- The graph of \( y > \frac{3}{4}x - 2 \) is a dashed line.
- One solution to the inequality is \((0,0)\).
- The graph intercepts the y-axis at [tex]\((0,-2)\)[/tex].
1. The slope of the line is -2.
- This statement is false. The slope of the line is given by the coefficient of \( x \) in the inequality \( y = \frac{3}{4} x - 2 \). Therefore, the correct slope is \(\frac{3}{4}\), not -2.
2. The graph of \( y > \frac{3}{4} x - 2 \) is a dashed line.
- This statement is true. The inequality is a strict inequality (greater than) which means the line itself is not included in the solution set. Thus, it is represented by a dashed line.
3. The area below the line is shaded.
- This statement is false. For the inequality \( y > \frac{3}{4} x - 2 \), the region above the line is shaded because the inequality is "greater than" \( \frac{3}{4} x - 2 \).
4. One solution to the inequality is \((0,0)\).
- This statement is true. To check if \((0,0)\) is a solution, substitute \( x = 0 \) and \( y = 0 \) into the inequality:
[tex]\[ 0 > \frac{3}{4}(0) - 2 \implies 0 > -2 \][/tex]
Since this statement is true, \((0,0)\) is indeed a solution.
5. The graph intercepts the y-axis at \((0,-2)\).
- This statement is true. The y-axis intercept occurs where \( x = 0 \). Substituting \( x = 0 \) into the equation \( y = \frac{3}{4} x - 2 \) yields:
[tex]\[ y = \frac{3}{4}(0) - 2 = -2 \][/tex]
Therefore, the y-intercept is at \((0, -2)\).
Based on this analysis, the three correct options are:
- The graph of \( y > \frac{3}{4}x - 2 \) is a dashed line.
- One solution to the inequality is \((0,0)\).
- The graph intercepts the y-axis at [tex]\((0,-2)\)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.