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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?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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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?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Determine slope of line q: Determine the slope of line q.\newlineThe equation of line q is given as y=83x−1y = \frac{8}{3}x - 1. The slope (mm) of a line in the slope-intercept form y=mx+by = mx + b is the coefficient of xx. Therefore, the slope of line q is 83\frac{8}{3}.
  2. Find slope of line rr: Find the slope of line rr.\newlineSince line rr is perpendicular to line qq, its slope will be the negative reciprocal of the slope of line qq. The negative reciprocal of 83\frac{8}{3} is −38-\frac{3}{8}.
  3. Use point-slope form: Use the point-slope form to find the equation of line rr. We have the slope of line rr −38-\frac{3}{8} and a point through which it passes (8,−7)(8, -7). The point-slope form of a line is (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 on the line. Plugging in the values, we get: (y−(−7))=−38(x−8)(y - (-7)) = -\frac{3}{8}(x - 8)
  4. Simplify to slope-intercept form: Simplify the equation to slope-intercept form.\newlineFirst, distribute the slope on the right side of the equation:\newliney+7=−38x+3y + 7 = -\frac{3}{8}x + 3\newlineNext, subtract 77 from both sides to solve for yy:\newliney=−38x+3−7y = -\frac{3}{8}x + 3 - 7\newliney=−38x−4y = -\frac{3}{8}x - 4

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