Which of the following may represent the curve x = 2y+ 3?

Options

A.
B.
C.
D.

Answer

To solve the question "Which of the following may represent the curve x = 2y + 3?", we will follow these steps:

### Step 1: Rearrange the given equation
The given equation is:
\[ x = 2y + 3 \]
We want to express this in the form of \( y = mx + c \) (the slope-intercept form).

### Step 2: Solve for y
To isolate \( y \), we can rearrange the equation:
\[ 2y = x - 3 \]
Now, divide both sides by 2:
\[ y = \frac{1}{2}x - \frac{3}{2} \]

### Step 3: Identify the slope and y-intercept
From the equation \( y = \frac{1}{2}x - \frac{3}{2} \):
- The slope \( m \) is \( \frac{1}{2} \).
- The y-intercept \( c \) is \( -\frac{3}{2} \).

### Step 4: Determine points for graphing
To graph this line, we can find two points:
1. When \( y = 0 \):
\[ 0 = \frac{1}{2}x - \frac{3}{2} \implies \frac{1}{2}x = \frac{3}{2} \implies x = 3 \]
So, the point is \( (3, 0) \).

2. When \( x = 0 \):
\[ y = \frac{1}{2}(0) - \frac{3}{2} = -\frac{3}{2} \]
So, the point is \( (0, -\frac{3}{2}) \).

### Step 5: Plot the points and draw the line
Now, we can plot the points \( (3, 0) \) and \( (0, -\frac{3}{2}) \) on the graph. Draw a straight line through these points.

### Step 6: Compare with options
Finally, we compare the graph we have drawn with the options provided in the question to identify which one matches our graph.

### Conclusion
The graph that matches our derived equation \( y = \frac{1}{2}x - \frac{3}{2} \) will be the correct representation of the curve \( x = 2y + 3 \).

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