Determine the Equation of a Line: Slope of 1/2 and Passing Through (5, 17.5)

To determine the line's equation, we'll follow these steps:

• Use the point-slope form of a line, given by $y - y_1 = m(x - x_1)$.
• Substitute $m = \frac{1}{2}$, $x_1 = 5$, and $y_1 = 17\frac{1}{2}$ into the equation.
• Solve for $y$ to put the equation in slope-intercept form.

Now, let's work through the steps:

Given the point $(5, 17\frac{1}{2})$ and slope $m = \frac{1}{2}$, our start point is the point-slope form:
$y - 17\frac{1}{2} = \frac{1}{2}(x - 5)$.

Convert the mixed number to an improper fraction: $17\frac{1}{2} = \frac{35}{2}$.

Thus, the equation becomes $y - \frac{35}{2} = \frac{1}{2}(x - 5)$.

Distribute the slope on the right-hand side:
$y - \frac{35}{2} = \frac{1}{2}x - \frac{5}{2}$.

To solve for $y$, add $\frac{35}{2}$ to both sides:
$y = \frac{1}{2}x - \frac{5}{2} + \frac{35}{2}$.

Combine the fractions on the right-hand side:
$y = \frac{1}{2}x + \frac{30}{2}$, which simplifies to $y = \frac{1}{2}x + 15$.

Therefore, the equation of the line in slope-intercept form is $y = \frac{1}{2}x + 15$.

Comparing this with the multiple-choice options, the correct answer is:

$y = \frac{1}{2}x + 15$