Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Let's analyze the given linear inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex].
1. The slope of the line is -2.
- The slope of a line in the equation [tex]\( y = mx + b \)[/tex] is given by the coefficient of [tex]\( x \)[/tex], which in this case is [tex]\( \frac{3}{4} \)[/tex]. Therefore, the slope of the line is [tex]\( \frac{3}{4} \)[/tex], not -2. This statement is false.
2. The graph of [tex]\( y = \frac{3}{4} x - 2 \)[/tex] is a dashed line.
- When graphing a linear inequality that uses the "greater than" (>) symbol, the boundary line [tex]\( y = \frac{3}{4} x - 2 \)[/tex] is drawn as a dashed line to indicate that points on the line are not included in the solution. Thus, this statement is true.
3. The area below the line is shaded.
- For [tex]\( y > \frac{3}{4} x - 2 \)[/tex], the shaded region consists of all points above the line [tex]\( y = \frac{3}{4} x - 2 \)[/tex] because we are looking for the [tex]\( y \)[/tex]-values that are greater than those on the line. Therefore, this statement is false.
4. One solution to the inequality is [tex]\( (0, 0) \)[/tex].
- To verify if [tex]\( (0, 0) \)[/tex] is a solution, we substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex]:
[tex]\[ 0 > \frac{3}{4}(0) - 2 \][/tex]
[tex]\[ 0 > -2 \][/tex]
This inequality is true. Therefore, [tex]\( (0, 0) \)[/tex] is indeed a solution of the inequality. This statement is true.
5. The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0, -2) \)[/tex].
- To find the [tex]\( y \)[/tex]-intercept of the line [tex]\( y = \frac{3}{4} x - 2 \)[/tex], we set [tex]\( x = 0 \)[/tex]:
[tex]\[ y = \frac{3}{4}(0) - 2 \][/tex]
[tex]\[ y = -2 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the graph is at [tex]\( (0, -2) \)[/tex]. This statement is true.
To summarize, the true statements about the inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex] are:
- The graph of [tex]\( y = \frac{3}{4} x - 2 \)[/tex] is a dashed line.
- One solution to the inequality is [tex]\( (0, 0) \)[/tex].
- The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0, -2) \)[/tex].
1. The slope of the line is -2.
- The slope of a line in the equation [tex]\( y = mx + b \)[/tex] is given by the coefficient of [tex]\( x \)[/tex], which in this case is [tex]\( \frac{3}{4} \)[/tex]. Therefore, the slope of the line is [tex]\( \frac{3}{4} \)[/tex], not -2. This statement is false.
2. The graph of [tex]\( y = \frac{3}{4} x - 2 \)[/tex] is a dashed line.
- When graphing a linear inequality that uses the "greater than" (>) symbol, the boundary line [tex]\( y = \frac{3}{4} x - 2 \)[/tex] is drawn as a dashed line to indicate that points on the line are not included in the solution. Thus, this statement is true.
3. The area below the line is shaded.
- For [tex]\( y > \frac{3}{4} x - 2 \)[/tex], the shaded region consists of all points above the line [tex]\( y = \frac{3}{4} x - 2 \)[/tex] because we are looking for the [tex]\( y \)[/tex]-values that are greater than those on the line. Therefore, this statement is false.
4. One solution to the inequality is [tex]\( (0, 0) \)[/tex].
- To verify if [tex]\( (0, 0) \)[/tex] is a solution, we substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex]:
[tex]\[ 0 > \frac{3}{4}(0) - 2 \][/tex]
[tex]\[ 0 > -2 \][/tex]
This inequality is true. Therefore, [tex]\( (0, 0) \)[/tex] is indeed a solution of the inequality. This statement is true.
5. The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0, -2) \)[/tex].
- To find the [tex]\( y \)[/tex]-intercept of the line [tex]\( y = \frac{3}{4} x - 2 \)[/tex], we set [tex]\( x = 0 \)[/tex]:
[tex]\[ y = \frac{3}{4}(0) - 2 \][/tex]
[tex]\[ y = -2 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the graph is at [tex]\( (0, -2) \)[/tex]. This statement is true.
To summarize, the true statements about the inequality [tex]\( y > \frac{3}{4} x - 2 \)[/tex] are:
- The graph of [tex]\( y = \frac{3}{4} x - 2 \)[/tex] is a dashed line.
- One solution to the inequality is [tex]\( (0, 0) \)[/tex].
- The graph intercepts the [tex]\( y \)[/tex]-axis at [tex]\( (0, -2) \)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.