Which equation represents the line that is the reflection of the line `y=2x-3` in the y-axis?

Options

A. `y=-2x-3`
B. `y=-2x+3`
C. `y=2x+3`
D. `y=3x-2`

Answer

To find the equation that represents the line which is the reflection of the line \( y = 2x - 3 \) in the y-axis, we can follow these steps:

### Step 1: Identify the given line
The equation of the given line is:
\[ y = 2x - 3 \]
This line has a slope of \( 2 \) and a y-intercept of \( -3 \).

### Step 2: Understand the reflection in the y-axis
When a line is reflected in the y-axis, the x-coordinates of all points on the line change sign. This means that if the original line has a slope \( m \), the reflected line will have a slope of \( -m \).

### Step 3: Determine the slope of the reflected line
The slope of the original line is \( 2 \). Therefore, the slope of the reflected line will be:
\[ \text{slope of reflected line} = -2 \]

### Step 4: Keep the y-intercept the same
The y-intercept of the original line is \( -3 \). Since the reflection in the y-axis does not change the y-intercept, the y-intercept of the reflected line will also be \( -3 \).

### Step 5: Write the equation of the reflected line
Using the slope-intercept form of a line \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can write the equation of the reflected line as:
\[ y = -2x - 3 \]

### Final Answer
Thus, the equation that represents the line that is the reflection of the line \( y = 2x - 3 \) in the y-axis is:
\[ \boxed{y = -2x - 3} \]

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