Question
Find the intercepts for the graph of the equation given.
xplus4yequals0
xplus4yequals0
Answers
GPT-4o mini
To find the intercepts of the equation \( x + 4y = 0 \), we need to determine both the x-intercept and the y-intercept.
1. **X-Intercept**: This is the point where the graph crosses the x-axis, which occurs when \( y = 0 \).
Substitute \( y = 0 \) into the equation:
\[
x + 4(0) = 0 \implies x = 0
\]
Thus, the x-intercept is \( (0, 0) \).
2. **Y-Intercept**: This is the point where the graph crosses the y-axis, which occurs when \( x = 0 \).
Substitute \( x = 0 \) into the equation:
\[
0 + 4y = 0 \implies 4y = 0 \implies y = 0
\]
Thus, the y-intercept is also \( (0, 0) \).
In conclusion, the intercepts for the graph of the equation \( x + 4y = 0 \) are:
- X-Intercept: \( (0, 0) \)
- Y-Intercept: \( (0, 0) \)
The graph passes through the origin.
1. **X-Intercept**: This is the point where the graph crosses the x-axis, which occurs when \( y = 0 \).
Substitute \( y = 0 \) into the equation:
\[
x + 4(0) = 0 \implies x = 0
\]
Thus, the x-intercept is \( (0, 0) \).
2. **Y-Intercept**: This is the point where the graph crosses the y-axis, which occurs when \( x = 0 \).
Substitute \( x = 0 \) into the equation:
\[
0 + 4y = 0 \implies 4y = 0 \implies y = 0
\]
Thus, the y-intercept is also \( (0, 0) \).
In conclusion, the intercepts for the graph of the equation \( x + 4y = 0 \) are:
- X-Intercept: \( (0, 0) \)
- Y-Intercept: \( (0, 0) \)
The graph passes through the origin.