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A line with a slope of 16-\frac{1}{6} passes through the point (10,3)(10,3). 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})

Full solution

Q. A line with a slope of 16-\frac{1}{6} passes through the point (10,3)(10,3). 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 yy1=m(xx1)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=16m = -\frac{1}{6} and the point (10,3)(10, 3). Substituting these values into the point-slope form, we get y3=(16)(x10)y - 3 = (-\frac{1}{6})(x - 10).
  3. Check for Simplification: Check for any simplification needed.\newlineIn this case, there is no further simplification required. The equation is already in its simplest form.

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