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A line that includes the point (9,9)(9,9) has a slope of 19\frac{1}{9}. 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 that includes the point (9,9)(9,9) has a slope of 19\frac{1}{9}. 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 Given Point and Slope: Substitute the given point and slope into the point-slope form.\newlineWe are given the point (9,9)(9, 9) and the slope 19\frac{1}{9}. Substituting these values into the point-slope form, we get y9=(19)(x9)y - 9 = \left(\frac{1}{9}\right)(x - 9).
  3. Check for Simplification: Check for any simplification needed.\newlineIn this case, there is no further simplification required, as the equation is already in its simplest form.

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