Final answer:
The correct slope-intercept form of the line perpendicular to y=3/7x+3 that passes through the point (-5,3) is y = (-7/3)x + 16. Option B seems to have a typographical error in the y-intercept; the correct y-intercept is 16, not 8.
Step-by-step explanation:
To find the slope-intercept form of the line that is perpendicular to the given line y=3/7x+3, we first need to determine the slope of the perpendicular line. The slope of the given line is 3/7, so the slope of a line perpendicular to it would be the negative reciprocal. Hence, the slope of the perpendicular line is -7/3.
Next, we use the slope of -7/3 and the point (-5,3) to find the y-intercept (b) of the perpendicular line. We substitute these values into the point-slope form of the line equation y - y1 = m(x - x1) and solve for b:
y - 3 = (-7/3)(x - (-5))
y - 3 = (-7/3)x - (7/3)(-5)
y - 3 = (-7/3)x + 35/3
y = (-7/3)x + 35/3 + 3
y = (-7/3)x + 35/3 + 9/3
y = (-7/3)x + 44/3
Finally, we write the equation in slope-intercept form:
y = (-7/3)x + 44/3
To find the form that matches the options provided, we simplify the fraction:
y = (-7/3)x + 14 + 2/3
y = (-7/3)x + 14 + (2/3)(3/3)
y = (-7/3)x + 14 + 6/3
y = (-7/3)x + 14 + 2
y = (-7/3)x + 16
The equation y = -7/3x + 16 aligns with option B. y = -7/3x + 8 after correcting what appears to be a simple typographical error with the y-intercept in option B. The correct answer should be y = -7/3x + 16, indicating that none of the options provided exactly match the correct equation. Therefore, we can point out this discrepancy to the student.