Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine which points lie on the graph of the equation \( y = \frac{3}{2} x - 4 \), we can substitute the \( x \) and \( y \) coordinates of each given point into the equation and see if the resulting equality holds true.
Let's evaluate each given point:
Point A \((-2, -2)\):
1. Substitute \( x = -2 \) into the equation:
[tex]\[ y = \frac{3}{2} (-2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = -3 - 4 = -7 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( -2 \).
[tex]\[ -7 \neq -2 \][/tex]
Thus, point A \((-2, -2)\) does not lie on the graph.
Point B \((-2, -4)\):
1. Substitute \( x = -2 \) into the equation:
[tex]\[ y = \frac{3}{2} (-2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = -3 - 4 = -7 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( -4 \).
[tex]\[ -7 \neq -4 \][/tex]
Thus, point B \((-2, -4)\) does not lie on the graph.
Point C \((2, -1)\):
1. Substitute \( x = 2 \) into the equation:
[tex]\[ y = \frac{3}{2} (2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = 3 - 4 = -1 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( -1 \).
[tex]\[ -1 = -1 \][/tex]
Thus, point C \((2, -1)\) lies on the graph.
Point D \((2, 1)\):
1. Substitute \( x = 2 \) into the equation:
[tex]\[ y = \frac{3}{2} (2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = 3 - 4 = -1 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( 1 \).
[tex]\[ -1 \neq 1 \][/tex]
Thus, point D \((2, 1)\) does not lie on the graph.
So, the point that lies on the graph of the equation \( y = \frac{3}{2} x - 4 \) is:
C) [tex]\((2, -1)\)[/tex].
Let's evaluate each given point:
Point A \((-2, -2)\):
1. Substitute \( x = -2 \) into the equation:
[tex]\[ y = \frac{3}{2} (-2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = -3 - 4 = -7 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( -2 \).
[tex]\[ -7 \neq -2 \][/tex]
Thus, point A \((-2, -2)\) does not lie on the graph.
Point B \((-2, -4)\):
1. Substitute \( x = -2 \) into the equation:
[tex]\[ y = \frac{3}{2} (-2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = -3 - 4 = -7 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( -4 \).
[tex]\[ -7 \neq -4 \][/tex]
Thus, point B \((-2, -4)\) does not lie on the graph.
Point C \((2, -1)\):
1. Substitute \( x = 2 \) into the equation:
[tex]\[ y = \frac{3}{2} (2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = 3 - 4 = -1 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( -1 \).
[tex]\[ -1 = -1 \][/tex]
Thus, point C \((2, -1)\) lies on the graph.
Point D \((2, 1)\):
1. Substitute \( x = 2 \) into the equation:
[tex]\[ y = \frac{3}{2} (2) - 4 \][/tex]
2. Calculate the right-hand side:
[tex]\[ y = 3 - 4 = -1 \][/tex]
3. Compare with the \( y \)-coordinate of the point, which is \( 1 \).
[tex]\[ -1 \neq 1 \][/tex]
Thus, point D \((2, 1)\) does not lie on the graph.
So, the point that lies on the graph of the equation \( y = \frac{3}{2} x - 4 \) is:
C) [tex]\((2, -1)\)[/tex].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.