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The equation for line c can be written as y=−7/3x+4

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The equation for line ccc can be written as y=37x+4y = -\frac{3}{7}x + 4. Perpendicular to line cc is line dd, which passes through the point (2,4)(2, 4). What is the equation of line dd?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.




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1 Answer

  1. Solution:

    1. Since line ddd is perpendicular to line cc, the slope of line dd will be the negative reciprocal of the slope of line ccc.
      • Slope of c=37c = -\frac{3}{7}
      • Slope of d=73d = \frac{7}{3}
    2. We use the point-slope form of the equation yy1=m(xx1)y – y_1 = m(x – x_1), where mmm is the slope and (x1,y1)=(2,4)(x_1, y_1) = (2, 4).
    3. Substitute the values:

      y4=73(x2)y – 4 = \frac{7}{3}(x – 2)

    4. Distribute 73\frac{7}{3}:

      y4=73x143y – 4 = \frac{7}{3}x – \frac{14}{3}

    5. Add 4 (or 123\frac{12}{3}) to both sides to solve for yyy:

      y=73x143+123y=73x23

    Answer:

    The equation of line ddd in slope-intercept form is:

    y=73x23