Final answer:
To find the equation of a line perpendicular to y = -1/4x + 9/2 that passes through the point (10, 2), the slope should be the negative reciprocal of -1/4, which is 4, resulting in y = 4x - 38. The student's provided answer suggests a different slope which could indicate an error or misunderstanding.
Step-by-step explanation:
The subject of the question is to find the equation of a line in slope-intercept form that is perpendicular to a given line and passes through a specific point. Given the equation of the first line y = -1/4x + 9/2, we know its slope is -1/4. Lines that are perpendicular to each other have slopes that are negative reciprocals. Therefore, the slope of the line we're looking for is 4 (the negative reciprocal of -1/4).
To find the equation, use the point-slope form first, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line. Plugging in the point (10, 2) and the slope 4, we get: y - 2 = 4(x - 10). Simplifying this yields y = 4x - 40 + 2, which further simplifies to y = 4x - 38.
However, based on the student's answer choices, it seems there might have been an error in either the point provided or in the understanding of how to apply the slope. If the student has specified that the correct answer is b) y = -4x + 38, this would suggest the slope should be negative, as in -4 (which is not the negative reciprocal of -1/4). This discrepancy needs to be reconciled to provide an accurate response.