Question

Julia found the equation of the line perpendicular to y = -2x² that passes through (5, –1). Analyze Julia's work and determine if she is correct. If not, identify her mistake.

Julia's Work:
y = 1/2x + b

Options:
1. y = 1/2 x
2. 5 = 1/2 (-1) + b
3. 5 = 1/2 b
4. b = 5.5
5. y = 1/2 x + 5.5

Select the correct statement:
A. Yes, she is correct.
B. No, she did not use the opposite reciprocal for the slope of the perpendicular line.
C. No, she did not substitute the correct x and y values.
D. No, she did not apply inverse operations to solve for the y-intercept.

Answer 1

Julia's mistake was that she used the slope 1/2 instead of the correct slope 1/4 to find the equation of the perpendicular line. The correct equation is y = 1/4x - 6.

Step-by-step explanation:

Julia is not correct. The equation of a line perpendicular to y = -2x² can be found by taking the opposite reciprocal of the slope of the given line. The given line has a slope of -4x. So, the perpendicular line will have a slope of 1/4x. We also know that this line passes through the point (5, -1). Using the point-slope form, we can substitute the values into the equation y - (-1) = 1/4x - 5. Simplifying, we get y = 1/4x - 6.

Julia's mistake was that she used the slope 1/2 instead of the correct slope 1/4. Therefore, the correct equation of the line perpendicular to y = -2x² that passes through (5, -1) is y = 1/4x - 6.