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The equation for line ff can be written as y=95x−2y = \frac{9}{5}x - 2. Perpendicular to line ff is line gg, which passes through the point (5,−3)(5,-3). What is the equation of line gg?\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 ff can be written as y=95x−2y = \frac{9}{5}x - 2. Perpendicular to line ff is line gg, which passes through the point (5,−3)(5,-3). What is the equation of line gg?\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 f: Determine the slope of line f.\newlineThe equation of line f is given as y=95x−2y = \frac{9}{5}x - 2. 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 f is 95\frac{9}{5}.
  2. Find slope of line g: Find the slope of line gg. Since line gg is perpendicular to line ff, its slope will be the negative reciprocal of the slope of line ff. The negative reciprocal of 95\frac{9}{5} is −59-\frac{5}{9}. Therefore, the slope of line gg is −59-\frac{5}{9}.
  3. Use point-slope form: Use the point-slope form to find the equation of line gg. We have the slope of line gg −59-\frac{5}{9} and a point through which it passes (5,−3)(5,-3). 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−(−3)=−59(x−5)y - (-3) = -\frac{5}{9}(x - 5).
  4. Simplify to slope-intercept form: Simplify the equation to slope-intercept form. First, distribute the slope on the right side: y+3=−59x+(59)⋅5y + 3 = -\frac{5}{9}x + (\frac{5}{9})\cdot5. Simplify the constant term: y+3=−59x+259y + 3 = -\frac{5}{9}x + \frac{25}{9}. Now, subtract 33 from both sides to get yy by itself: y=−59x+259−279y = -\frac{5}{9}x + \frac{25}{9} - \frac{27}{9}. Combine the constant terms: y=−59x−29y = -\frac{5}{9}x - \frac{2}{9}.

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