If ax -4y =-6 has a slope of `-3/2` what is the value of a

Options

A. 6
B. 3
C. `-6`
D. `-3`

Answer

To solve the problem, we need to find the value of \( a \) in the equation \( ax - 4y = -6 \) given that the slope of the line is \( -\frac{3}{2} \).

### Step-by-Step Solution:

1. **Identify the equation and slope**: We have the equation \( ax - 4y = -6 \) and the slope \( m = -\frac{3}{2} \).

2. **Rearrange the equation into slope-intercept form**: The slope-intercept form of a line is given by \( y = mx + b \). We need to solve for \( y \) in terms of \( x \):
\[ ax - 4y = -6 \]
Rearranging gives:
\[ -4y = -ax - 6 \]
Dividing by -4:
\[ y = \frac{a}{4}x + \frac{3}{2} \]

3. **Identify the slope from the rearranged equation**: From the equation \( y = \frac{a}{4}x + \frac{3}{2} \), we can see that the slope \( m \) is \( \frac{a}{4} \).

4. **Set the slopes equal to each other**: Since we know the slope is also given as \( -\frac{3}{2} \), we can set up the equation:
\[ \frac{a}{4} = -\frac{3}{2} \]

5. **Solve for \( a \)**: To find \( a \), we can multiply both sides by 4:
\[ a = -\frac{3}{2} \times 4 \]
Simplifying this gives:
\[ a = -6 \]

### Conclusion:
The value of \( a \) is \( -6 \).