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Math Asked by a SnapAndSolve user · about 1 hour ago

Mona sketches a line that passes through the point (-7, 5) and that is perpendicular to the line passing...

Mona sketches a line that passes through the point (-7, 5) and that is perpendicular to the line passing through the points (-3/2, 31/4) and (7/2, -39/4). What is the equation of Mona's line?
A. y = -2/7x + 3
B. y = 2/7x + 3
C. y = 2/7x + 7
D. y = -2/7x + 7

Answer

To find the equation of Mona's line, we first need to determine the slope of the line passing through the points (-3/2, 31/4) and (7/2, -39/4). The slope (m) is calculated as follows:

  1. Calculate the slope of the given line:
    m = ((-39/4) - (31/4)) / ((7/2) - (-3/2)) = (-70/4) / (10/2) = -35/10 = -7/2.
  2. The slope of the line perpendicular to this line is the negative reciprocal:
    m_perpendicular = 2/7.
  3. Using the point-slope form of the equation of a line (y - y1 = m(x - x1)) with the point (-7, 5):
    y - 5 = (2/7)(x + 7).
  4. Simplify to get the equation in slope-intercept form:
    y = (2/7)x + 2 + 5 = (2/7)x + 7.

Thus, the equation of Mona's line is y = (2/7)x + 7, which corresponds to option C.

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