To write the equation of a line in slope-intercept form, which is \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), we can start by using the given information:
- The slope \( m = -\frac{1}{2} \)
- The line passes through the point \( (1, 2) \)
We can substitute the given point \((x, y) = (1, 2)\) and the slope into the equation to find \( b \) (the y-intercept):
\[ y = mx + b \] Plugging in the values:
\[ 2 = -\frac{1}{2}(1) + b \]
Now, simplify:
\[ 2 = -\frac{1}{2} + b \]
To isolate \( b \), add \(\frac{1}{2}\) to both sides:
\[ b = 2 + \frac{1}{2} \]
Converting 2 to a fraction gives us:
\[ b = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]
Now, converting \(\frac{5}{2}\) to a decimal gives us:
\[ b = 2.5 \]
Thus, the y-intercept of the line, rounded to the nearest tenth, is 2.5.