If point `(a, a + 2)` lies on the line `y = 3x + 5,` then distance of the point from y-axis is

Options

A. `3/2`
B. 3
C. `1/2`
D. `7/2`

Answer

To find the distance of the point \((a, a + 2)\) from the y-axis, we first need to determine the value of \(a\) such that the point lies on the line defined by the equation \(y = 3x + 5\).

### Step-by-Step Solution:

1. **Substituting the Point into the Line Equation**:
The point \((a, a + 2)\) lies on the line \(y = 3x + 5\). Therefore, we substitute \(x = a\) and \(y = a + 2\) into the equation:
\[ a + 2 = 3a + 5 \]

2. **Rearranging the Equation**:
To solve for \(a\), we rearrange the equation:
\[ a + 2 - 3a = 5 \]
Simplifying this gives:
\[ -2a + 2 = 5 \]

3. **Isolating \(a\)**:
Next, we isolate \(a\) by moving the constant term to the other side:
\[ -2a = 5 - 2 \]
\[ -2a = 3 \]
Dividing both sides by -2:
\[ a = -\frac{3}{2} \]

4. **Finding the Coordinates of the Point**:
Now that we have \(a\), we can find the coordinates of the point:
\[ x = a = -\frac{3}{2} \]
\[ y = a + 2 = -\frac{3}{2} + 2 = -\frac{3}{2} + \frac{4}{2} = \frac{1}{2} \]
So the point is \(\left(-\frac{3}{2}, \frac{1}{2}\right)\).

5. **Calculating the Distance from the y-axis**:
The distance of a point \((x, y)\) from the y-axis is given by the absolute value of its x-coordinate. Therefore, the distance from the y-axis is:
\[ \text{Distance} = |x| = \left| -\frac{3}{2} \right| = \frac{3}{2} \]

### Final Answer:
The distance of the point from the y-axis is \(\frac{3}{2}\).

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