Question
\( P ( 2 , - 3 ) , y = - \frac { 1 } { 2 } x + 4 \)
Ask by Herrera Gordon. in Guam
Nov 17,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The point \( P(2, -3) \) does not lie on the line \( y = -\frac{1}{2}x + 4 \).
Solution
It looks like you have a point \( P(2, -3) \) and a linear equation \( y = -\frac{1}{2}x + 4 \).
If you want to determine whether the point \( P \) lies on the line defined by the equation, you can substitute the x-coordinate of the point into the equation and see if the resulting y-coordinate matches the y-coordinate of the point.
1. Substitute \( x = 2 \) into the equation:
\[
y = -\frac{1}{2}(2) + 4
\]
2. Calculate:
\[
y = -1 + 4 = 3
\]
The calculated y-value is \( 3 \), while the y-coordinate of point \( P \) is \( -3 \). Since \( 3 \neq -3 \), the point \( P(2, -3) \) does not lie on the line given by the equation \( y = -\frac{1}{2}x + 4 \).
If you have any other questions or need further assistance, feel free to ask!
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Simplify this solution The Deep Dive
Did you know that the point \( P(2, -3) \) can help us check if it lies on the given line defined by \( y = -\frac{1}{2}x + 4 \)? By substituting \( x = 2 \) into the equation, we find the corresponding \( y \) value: \( y = -\frac{1}{2}(2) + 4 = 3 \). Since \( -3 \neq 3 \), point \( P \) does not lie on this line. To visualize better, you can sketch the line on a graph. Start with the y-intercept at \( (0, 4) \) and use the slope \( -\frac{1}{2} \) to find another point. From \( (0, 4) \), move down 1 unit and to the right 2 units, landing at \( (2, 3) \). Now, you'll see where \( P \) fits in relation to the line!
