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Line gg has an equation of y=−29x+6y = -\frac{2}{9}x + 6. Parallel to line gg is line hh, which passes through the point (3,2)(3,2). What is the equation of line hh?\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. Line gg has an equation of y=−29x+6y = -\frac{2}{9}x + 6. Parallel to line gg is line hh, which passes through the point (3,2)(3,2). What is the equation of line hh?\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 g: Determine the slope of line g. Line g has an equation of y=−29x+6y = -\frac{2}{9}x + 6. The slope of a line in the form y=mx+by = mx + b is mm, where mm is the coefficient of xx. The slope of line g is −29-\frac{2}{9}.
  2. Determine Slope of Line hh: Since line hh is parallel to line gg, it will have the same slope. Parallel lines have the same slope. Therefore, the slope of line hh is also −29-\frac{2}{9}.
  3. Use Point-Slope Form: Use the point-slope form to find the equation of line hh. 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 slope m=−29m = -\frac{2}{9} and the point (3,2)(3, 2). Plugging these values into the point-slope form gives us y−2=−29(x−3)y - 2 = -\frac{2}{9}(x - 3).
  4. Simplify Equation to Slope-Intercept Form: Simplify the equation to get it into slope-intercept form y=mx+by = mx + b.
    y−2=−29(x−3)y - 2 = -\frac{2}{9}(x - 3)
    y−2=−29x+29(3)y - 2 = -\frac{2}{9}x + \frac{2}{9}(3)
    y−2=−29x+69y - 2 = -\frac{2}{9}x + \frac{6}{9}
    y−2=−29x+23y - 2 = -\frac{2}{9}x + \frac{2}{3}
    Now, add 22 to both sides to solve for yy.
    y=−29x+23+2y = -\frac{2}{9}x + \frac{2}{3} + 2
    y=−29x+23+63y = -\frac{2}{9}x + \frac{2}{3} + \frac{6}{3}
    y=−29x+83y = -\frac{2}{9}x + \frac{8}{3}

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