If a striaght line passes through the points (`-1/2,1)` and (1,2) then its x-intercept is

Options

A. `-2`
B. `-1`
C. 2
D. 1

Explanation

To find the x-intercept of the straight line that passes through the points \((-1/2, 1)\) and \((1, 2)\), we will follow these steps:

### Step 1: Identify the points
Let the points be:
- \( (x_1, y_1) = (-\frac{1}{2}, 1) \)
- \( (x_2, y_2) = (1, 2) \)

### Step 2: Use the two-point form of the equation of a line
The two-point form of the equation of a line is given by:
\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) \]

### Step 3: Substitute the values into the equation
Substituting the values into the equation:
\[ y - 1 = \frac{2 - 1}{1 - (-\frac{1}{2})}(x - (-\frac{1}{2})) \]
Calculating the slope:
\[ \frac{2 - 1}{1 + \frac{1}{2}} = \frac{1}{\frac{3}{2}} = \frac{2}{3} \]
So the equation becomes:
\[ y - 1 = \frac{2}{3}(x + \frac{1}{2}) \]

### Step 4: Simplify the equation
Distributing \(\frac{2}{3}\):
\[ y - 1 = \frac{2}{3}x + \frac{2}{6} \]
\[ y - 1 = \frac{2}{3}x + \frac{1}{3} \]
Adding 1 to both sides:
\[ y = \frac{2}{3}x + \frac{1}{3} + 1 \]
\[ y = \frac{2}{3}x + \frac{4}{3} \]

### Step 5: Rearranging to standard form
To find the x-intercept, we can rearrange the equation into standard form:
\[ 2x - 3y = -4 \]

### Step 6: Find the x-intercept
To find the x-intercept, set \(y = 0\):
\[ 2x - 3(0) = -4 \]
\[ 2x = -4 \]
\[ x = -2 \]

### Conclusion
The x-intercept of the line is \(-2\).

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