Determine the Linear Equation: Given Slope 1.5 and Point (3, 7.5)

To solve the problem of finding the equation of the line:

• Step 1: Identify the given information: slope $m = 1\frac{1}{2} = \frac{3}{2}$, and point $(x_1, y_1) = (3, 7\frac{1}{2}) = (3, \frac{15}{2})$.
• Step 2: Use the point-slope formula $y - y_1 = m(x - x_1)$.
• Step 3: Substitute the given slope and point into the formula: $y - \frac{15}{2} = \frac{3}{2}(x - 3)$.
• Step 4: Distribute the slope on the right side: $y - \frac{15}{2} = \frac{3}{2}x - \frac{9}{2}$.
• Step 5: Add $\frac{15}{2}$ to both sides to solve for $y$: $y = \frac{3}{2}x - \frac{9}{2} + \frac{15}{2}$.
• Step 6: Simplify the right side: $y = \frac{3}{2}x + 3$.
• Step 7: Compare this expression to the provided choices to find a match. The form is the same as choice $y=1\frac{1}{2}(x+2)$, rewritten correctly as $y = \frac{3}{2}(x + 2)$.

Therefore, the expression that corresponds to the line is $y = 1\frac{1}{2}(x+2)$.