The linear equation such that each point on its graph as an ordinate four times its abscissa is :

Options

A. `y + 4 x = 0 `
B. ` y = 4 x`
C. ` x = 4y`
D. ` x + 4 y = 0 `

Answer

To solve the problem, we need to find a linear equation where the ordinate (y-coordinate) is four times the abscissa (x-coordinate). Let's break it down step by step:

### Step 1: Understand the terms
- **Abscissa** refers to the x-coordinate of a point on the graph.
- **Ordinate** refers to the y-coordinate of a point on the graph.

### Step 2: Set up the relationship
According to the problem, the ordinate (y) is four times the abscissa (x). We can express this relationship mathematically as:
\[ y = 4x \]

### Step 3: Identify the linear equation
The equation \( y = 4x \) is a linear equation in slope-intercept form (y = mx + b), where:
- **m** (the slope) is 4, and
- **b** (the y-intercept) is 0.

### Step 4: Verify with some values
To confirm that this equation holds true, we can substitute some values for x and calculate the corresponding y values:
- If \( x = 0 \), then \( y = 4(0) = 0 \)
- If \( x = 1 \), then \( y = 4(1) = 4 \)
- If \( x = 2 \), then \( y = 4(2) = 8 \)
- If \( x = 3 \), then \( y = 4(3) = 12 \)

These calculations show that for each value of x, the value of y is indeed four times x.

### Conclusion
Thus, the linear equation such that each point on its graph has an ordinate four times its abscissa is:
\[ y = 4x \]

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