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 find the value of \( a \) in the equation \( ax - 4y = -6 \) given that the slope is \( \frac{3}{2} \), we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
We start with the equation:
\[ ax - 4y = -6 \]
We need to isolate \( y \) to express the equation in the form \( y = mx + b \), where \( m \) represents the slope.

### Step 2: Isolate \( y \)
To isolate \( y \), we can rearrange the equation:
\[ -4y = -ax - 6 \]
Now, divide both sides by -4:
\[ y = \frac{a}{4}x + \frac{6}{4} \]
This simplifies to:
\[ y = \frac{a}{4}x + \frac{3}{2} \]

### Step 3: Identify the slope
From the equation \( y = \frac{a}{4}x + \frac{3}{2} \), we can see that the slope \( m \) is:
\[ m = \frac{a}{4} \]
We know from the problem that the slope is \( \frac{3}{2} \).

### Step 4: Set the slopes equal
Now, we can set the two expressions for the slope equal to each other:
\[ \frac{a}{4} = \frac{3}{2} \]

### Step 5: Solve for \( a \)
To solve for \( a \), we can cross-multiply:
\[ a \cdot 2 = 3 \cdot 4 \]
This simplifies to:
\[ 2a = 12 \]
Now, divide both sides by 2:
\[ a = 6 \]

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