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The equation of line qq is y=16x−5y = \frac{1}{6}x - 5. Line rr, which is parallel to line qq, includes the point (6,2)(6,2). 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 of line qq is y=16x−5y = \frac{1}{6}x - 5. Line rr, which is parallel to line qq, includes the point (6,2)(6,2). 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. Find slope of line q: Determine the slope of line q. Line q has the equation y=16x−5y = \frac{1}{6}x - 5. The slope of line q is the coefficient of xx, which is 16\frac{1}{6}.
  2. Determine slope of line rr: Since line rr is parallel to line qq, it must have the same slope. The slope of line rr is therefore also 16\frac{1}{6}.
  3. Use point-slope form: Use the point-slope form to find the equation of line rr. 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 a point on the line. We have the point (6,2)(6,2) and the slope 16\frac{1}{6}.
  4. Substitute slope and point: Substitute the slope and the point into the point-slope form.\newlineUsing the point (6,2)(6,2) and the slope 16\frac{1}{6}, the equation becomes y−2=16(x−6)y - 2 = \frac{1}{6}(x - 6).
  5. Simplify equation: Simplify the equation to get it into slope-intercept form, y=mx+by = mx + b.\newliney−2=16x−16(6)y - 2 = \frac{1}{6}x - \frac{1}{6}(6)\newliney−2=16x−1y - 2 = \frac{1}{6}x - 1\newliney=16x−1+2y = \frac{1}{6}x - 1 + 2\newliney=16x+1y = \frac{1}{6}x + 1

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