Find the equation of a line of unit slope and passing through the origin.

Options

A. `y=x`
B. `x+y=0`
C. `x=y+1`
D. `x=1/2 y+1`

Answer

To find the equation of a line with a unit slope that passes through the origin, we can follow these steps:

### Step 1: Identify the slope (m) and the y-intercept (c)
The problem states that the slope of the line is 1 (unit slope) and that it passes through the origin. Therefore, we have:
- Slope (m) = 1
- y-intercept (c) = 0 (since it passes through the origin)

### Step 2: Use the slope-intercept form of the equation of a line
The slope-intercept form of the equation of a line is given by:
\[ y = mx + c \]
where:
- \( y \) is the dependent variable,
- \( m \) is the slope,
- \( x \) is the independent variable,
- \( c \) is the y-intercept.

### Step 3: Substitute the values of m and c into the equation
Now, we substitute the values we identified in Step 1 into the slope-intercept form:
\[ y = 1 \cdot x + 0 \]

### Step 4: Simplify the equation
This simplifies to:
\[ y = x \]

### Final Answer
Thus, the equation of the line with a unit slope that passes through the origin is:
\[ y = x \]

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