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There is a line that includes the point (8,10)(-8,10) and has a slope of 110\frac{1}{10}. 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. There is a line that includes the point (8,10)(-8,10) and has a slope of 110\frac{1}{10}. 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 Point and Slope: Substitute the given point and slope into the point-slope form. We have the point (8,10)(-8, 10) and the slope 110\frac{1}{10}. Substituting these values into the point-slope form, we get y10=(110)(x(8))y - 10 = \left(\frac{1}{10}\right)(x - (-8)).
  3. Simplify Equation: Simplify the equation.\newlineThe equation simplifies to y10=(110)(x+8)y - 10 = \left(\frac{1}{10}\right)(x + 8). There is no need to simplify further as the equation is already in point-slope form and the fractions are in their simplest form.

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