In the standard (x,y) coordinate plane, what is the slope of the line `3x + 8y = 5`?

Options

A. `-3`
B. `-3/8`
C. `3/5`
D. `3`

Answer

To find the slope of the line given by the equation \(3x + 8y = 5\), we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is given by the equation \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. We need to isolate \(y\) in the equation \(3x + 8y = 5\).

### Step 2: Isolate \(y\)
Start by moving \(3x\) to the right side of the equation:
\[ 8y = 5 - 3x \]

### Step 3: Divide by the coefficient of \(y\)
Next, divide every term by \(8\) to solve for \(y\):
\[ y = -\frac{3}{8}x + \frac{5}{8} \]

### Step 4: Identify the slope
Now that we have the equation in the form \(y = mx + c\), we can identify the slope \(m\). From the equation, we see that:
\[ m = -\frac{3}{8} \]

### Conclusion
Thus, the slope of the line \(3x + 8y = 5\) is \(-\frac{3}{8}\).

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