The equation of a straight line which makes an angle 45° with the x-axis with y-intercept 101 units is

Options

A. 10x + 101y = 1
B. 101x + y = 1
C. x + y - 101 = 0
D. x - y + 101 = 0

Answer

To find the equation of a straight line that makes an angle of 45° with the x-axis and has a y-intercept of 101 units, we can follow these steps:

### Step 1: Understand the slope
The slope (m) of a line that makes an angle θ with the x-axis is given by the formula:
\[ m = \tan(\theta) \]
For an angle of 45°, we have:
\[ m = \tan(45°) = 1 \]

### Step 2: Identify the y-intercept
The y-intercept (c) is the point where the line crosses the y-axis. According to the problem, the y-intercept is given as:
\[ c = 101 \]

### Step 3: Write the equation of the line
The general form of the equation of a straight line is:
\[ y = mx + c \]
Substituting the values of m and c into this equation, we get:
\[ y = 1x + 101 \]
or simply:
\[ y = x + 101 \]

### Step 4: Rearranging the equation (optional)
If we want to express the equation in standard form, we can rearrange it:
\[ y - x - 101 = 0 \]
This can also be written as:
\[ -x + y - 101 = 0 \]

### Final Answer
The equation of the straight line that makes an angle of 45° with the x-axis and has a y-intercept of 101 units is:
\[ y = x + 101 \]
or in standard form:
\[ -x + y - 101 = 0 \]

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