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The equation of line f is y+3=(1)/(6)(x-2). Parallel to line f is line g, which passes through the point (-6,1). What is the equation of line g ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

The equation of line f f is y+3=16(x−2) y+3=\frac{1}{6}(x-2) . Parallel to line f f is line g g , which passes through the point (−6,1) (-6,1) . What is the equation of line g g ?\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 f f is y+3=16(x−2) y+3=\frac{1}{6}(x-2) . Parallel to line f f is line g g , which passes through the point (−6,1) (-6,1) . What is the equation of line g g ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Identify slope of line ff: Identify the slope of line ff from its equation.\newlineThe equation of line ff is given in point-slope form: y+3=16(x−2)y + 3 = \frac{1}{6}(x - 2).\newlineThe slope of line ff is the coefficient of (x−2)(x - 2), which is 16\frac{1}{6}.\newlineSince line gg is parallel to line ff, it will have the same slope.
  2. Write point-slope form of line g: Write the point-slope form of line g using the slope and the point it passes through.\newlineThe slope of line g is 16\frac{1}{6}, and it passes through the point (−6,1)(-6,1).\newlineThe point-slope form 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.\newlineSubstitute m=16m = \frac{1}{6} and the point (−6,1)(-6, 1) into the equation.\newliney−1=(16)(x−(−6))y - 1 = \left(\frac{1}{6}\right)(x - (-6))
  3. Simplify equation of line g: Simplify the equation of line g to slope-intercept form. \newliney−1=16(x+6)y - 1 = \frac{1}{6}(x + 6)\newlineDistribute the slope 16\frac{1}{6} across (x+6)(x + 6).\newliney−1=16x+16⋅6y - 1 = \frac{1}{6}x + \frac{1}{6}\cdot6\newliney−1=16x+1y - 1 = \frac{1}{6}x + 1\newlineAdd 11 to both sides to solve for yy.\newliney=16x+1+1y = \frac{1}{6}x + 1 + 1\newliney=16x+2y = \frac{1}{6}x + 2

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