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A line with a slope of −19-\frac{1}{9} passes through the point (−3,6)(-3,6). What is its equation in point-slope form?\newlineUse the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.\newliney−‾=‾(x−‾)y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})

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Point-slope form: write an equationright chevron icon

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Q. A line with a slope of −19-\frac{1}{9} passes through the point (−3,6)(-3,6). What is its equation in point-slope form?\newlineUse the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.\newliney−‾=‾(x−‾)y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
  1. Identify Point-Slope Form: Identify the point-slope form of a linear equation.\newlineThe point-slope form of a linear equation is given by the formula y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope of the line and (x1,y1)(x_1, y_1) is a point on the line.
  2. Substitute Slope and Point: Substitute the given slope and point into the point-slope form.\newlineWe are given the slope m=−19m = -\frac{1}{9} and the point (x1,y1)=(−3,6)(x_1, y_1) = (-3, 6). Substituting these values into the point-slope form, we get:\newliney−6=(−19)(x−(−3))y - 6 = (-\frac{1}{9})(x - (-3))
  3. Simplify Equation: Simplify the equation.\newlineThe equation simplifies to:\newliney−6=(−19)(x+3)y - 6 = \left(-\frac{1}{9}\right)(x + 3)\newlineThis is the equation of the line in point-slope form.

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