To write the equation of a line in slope-intercept form (which is \( y = mx + b \)), we need to know the slope \( m \) and the y-intercept \( b \).
Given:
- Slope \( m = -\frac{1}{2} \)
- Point \( (1, 2) \)
We can use the point-slope formula to find the y-intercept. The point-slope formula is given by:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the point the line passes through. Substituting in the values we have:
- \( x_1 = 1 \)
- \( y_1 = 2 \)
- \( m = -\frac{1}{2} \)
Substituting these into the formula:
\[ y - 2 = -\frac{1}{2}(x - 1) \]
Now, we simplify this equation:
\[ y - 2 = -\frac{1}{2}x + \frac{1}{2} \]
Now, add 2 to both sides:
\[ y = -\frac{1}{2}x + \frac{1}{2} + 2 \]
To combine the constants, convert 2 into a fraction with a denominator of 2:
\[ 2 = \frac{4}{2} \]
So now we have:
\[ y = -\frac{1}{2}x + \frac{1}{2} + \frac{4}{2} \]
This simplifies to:
\[ y = -\frac{1}{2}x + \frac{5}{2} \]
Now we need to determine the y-intercept \( b \):
\[ b = \frac{5}{2} = 2.5 \]
Thus, rounding to the nearest tenth, the y-intercept is:
\[ \boxed{2.5} \]