Final answer:
To write an equation in standard form given the slope -1/2 and point (2,4), use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substitute the values into the formula, distribute the negative sign, and rearrange the terms to obtain the equation in standard form y + (1/2)x = 5.
Step-by-step explanation:
To write an equation in standard form given the slope and a point, you can use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. In this case, the given slope is -1/2 and the given point is (2,4). Substituting these values into the formula, we get y - 4 = -(1/2)(x - 2). To convert this equation to standard form, we can distribute the negative sign and simplify: y - 4 = (-1/2)x + 1. Rearranging the terms, we obtain the equation in standard form as: y + (1/2)x = 5. Therefore, the correct answer is option a) y = -1/2x + 5.