Question
What is the slope of the line represented by the equation 3x+4y= 12?
Responses
–43
negative 4 over 3
–34
negative 3 over 4
34
3 over 4
43
Responses
–43
negative 4 over 3
–34
negative 3 over 4
34
3 over 4
43
Answers
GPT-4o mini
To find the slope of the line represented by the equation \(3x + 4y = 12\), we need to rewrite the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.
Starting with the given equation:
\[ 3x + 4y = 12 \]
Now, isolate \(y\):
1. Subtract \(3x\) from both sides:
\[ 4y = -3x + 12 \]
2. Divide every term by \(4\):
\[ y = -\frac{3}{4}x + 3 \]
Now, we can see that the slope \(m\) is \(-\frac{3}{4}\).
Thus, the slope of the line is **negative 3 over 4**.
Starting with the given equation:
\[ 3x + 4y = 12 \]
Now, isolate \(y\):
1. Subtract \(3x\) from both sides:
\[ 4y = -3x + 12 \]
2. Divide every term by \(4\):
\[ y = -\frac{3}{4}x + 3 \]
Now, we can see that the slope \(m\) is \(-\frac{3}{4}\).
Thus, the slope of the line is **negative 3 over 4**.