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What is the equation of the line that passes through the point (6,3) and has a slope of (3)/(2) ? Answer:

What is the equation of the line that passes through the point (6,3) (6,3) and has a slope of 32 \frac{3}{2} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (6,3) (6,3) and has a slope of 32 \frac{3}{2} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope mm and the point (x1,y1)(x_1, y_1) through which the line passes.\newlineThe slope mm is given as 32\frac{3}{2}, and the point is (6,3)(6,3).
  2. Use point-slope form: Use the point-slope form of the equation of a line to start solving for the equation.\newlineThe point-slope form is: y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is the point the line passes through.
  3. Substitute slope and point: Substitute the slope (32)(\frac{3}{2}) and the point (6,3)(6,3) into the point-slope form.\newliney−3=32(x−6)y - 3 = \frac{3}{2}(x - 6)
  4. Distribute slope: Distribute the slope (32)(\frac{3}{2}) on the right side of the equation.\newliney−3=32x−32×6y - 3 = \frac{3}{2}x - \frac{3}{2}\times6\newliney−3=32x−9y - 3 = \frac{3}{2}x - 9
  5. Add to solve for y: Add 33 to both sides of the equation to solve for y in terms of x.\newliney=32x−9+3y = \frac{3}{2}x - 9 + 3\newliney=32x−6y = \frac{3}{2}x - 6

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