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The equation for line qq can be written as y=83x−1y= \frac{8}{3}x-1. Line rr is perpendicular to line qq and passes through (8,−7)(8, -7). What is the equation of line rr? 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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Full solution

Q. The equation for line qq can be written as y=83x−1y= \frac{8}{3}x-1. Line rr is perpendicular to line qq and passes through (8,−7)(8, -7). What is the equation of line rr? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Find Perpendicular Slope: Line qq has a slope of 83\frac{8}{3}. Since line rr is perpendicular to line qq, its slope will be the negative reciprocal of 83\frac{8}{3}.
  2. Calculate Slope of Line rr: The negative reciprocal of 83\frac{8}{3} is −38-\frac{3}{8}. This is the slope of line rr.
  3. Use Point-Slope Form: Using the point-slope form, y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point (8,−7)(8, -7), we plug in the values to find the equation of line rr.
  4. Simplify Equation: y−(−7)=−38(x−8)y - (-7) = -\frac{3}{8}(x - 8)
  5. Simplify Equation: y−(−7)=−38(x−8)y - (-7) = -\frac{3}{8}(x - 8) Simplify the equation to get y+7=−38x+3y + 7 = -\frac{3}{8}x + 3

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