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The equation for line gg can be written as y=310x−8y = \frac{3}{10}x - 8. Perpendicular to line gg is line hh, which passes through the point (3,−9)(3,-9). 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. The equation for line gg can be written as y=310x−8y = \frac{3}{10}x - 8. Perpendicular to line gg is line hh, which passes through the point (3,−9)(3,-9). 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. Determine slope of line g: Determine the slope of line g.\newlineThe equation of line g is given as y=310x−8y = \frac{3}{10}x - 8. 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 g is 310\frac{3}{10}.
  2. Find slope of line h: Find the slope of line h. Since line h is perpendicular to line g, its slope will be the negative reciprocal of the slope of line g. The negative reciprocal of 310\frac{3}{10} is −103-\frac{10}{3}.
  3. Use point-slope form: Use the point-slope form to find the equation of line hh. Line hh passes through the point (3,−9)(3,-9) and has a slope of −103-\frac{10}{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 a point on the line. Plugging in the values, we get y−(−9)=−103(x−3)y - (-9) = -\frac{10}{3}(x - 3).
  4. Simplify equation of line h: Simplify the equation of line h.\newlineFirst, distribute the slope on the right side of the equation: y+9=−103(x−3)y + 9 = -\frac{10}{3}(x - 3).\newlineNext, distribute −103-\frac{10}{3} inside the parentheses: y+9=−103x+10y + 9 = -\frac{10}{3}x + 10.\newlineThen, subtract 99 from both sides to get the equation in slope-intercept form: y=−103x+10−9y = -\frac{10}{3}x + 10 - 9.\newlineFinally, simplify the constant term: y=−103x+1y = -\frac{10}{3}x + 1.

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