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The equation of line gg is y=−13x−8y = -\frac{1}{3}x - 8. Line hh includes the point (−10,6)(-10,6) and is parallel to line gg. 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 of line gg is y=−13x−8y = -\frac{1}{3}x - 8. Line hh includes the point (−10,6)(-10,6) and is parallel to line gg. 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. The equation of line g is given as y=−13x−8y = -\frac{1}{3}x - 8. The slope of line g is the coefficient of xx in the equation. Slope of line g: −13-\frac{1}{3}
  2. Determine Slope of Line hh: Since line hh is parallel to line gg, it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line hh is also −13-\frac{1}{3}.
  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=−13m = -\frac{1}{3} and the point (−10,6)(-10, 6). Plug these values into the point-slope form. y−6=−13(x−(−10))y - 6 = -\frac{1}{3}(x - (-10))
  4. Simplify Equation: Simplify the equation to get the slope-intercept form, y=mx+by = mx + b.\newliney−6=−13(x+10)y - 6 = -\frac{1}{3}(x + 10)\newliney−6=−13x−103y - 6 = -\frac{1}{3}x - \frac{10}{3}\newlineAdd 66 to both sides to isolate yy.\newliney=−13x−103+6y = -\frac{1}{3}x - \frac{10}{3} + 6
  5. Convert 66 to Fraction: Convert 66 to a fraction with a denominator of 33 to combine with −103-\frac{10}{3}. 66 is the same as 183\frac{18}{3}. y=−13x−103+183y = -\frac{1}{3}x - \frac{10}{3} + \frac{18}{3}
  6. Combine Fractions: Combine the fractions.\newliney=−13x+83y = -\frac{1}{3}x + \frac{8}{3}\newlineThis is the equation of line hh in slope-intercept form.

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