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Use point-slope form to write the equation of a line that passes through the point (7,7) with slope (2)/(3). Answer:

Use point-slope form to write the equation of a line that passes through the point (7,7) (7,7) with slope 23 \frac{2}{3} .\newlineAnswer:

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Full solution

Q. Use point-slope form to write the equation of a line that passes through the point (7,7) (7,7) with slope 23 \frac{2}{3} .\newlineAnswer:
  1. Recall Point-Slope Form: Recall the point-slope form of a line's equation. The point-slope form of a line's equation is given by y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.
  2. Identify Slope and Point: Identify the slope mm and the point (x1,y1)(x_1, y_1) through which the line passes.\newlineFrom the problem, we have the slope m=23m = \frac{2}{3} and the point (x1,y1)=(7,7)(x_1, y_1) = (7, 7).
  3. Substitute into Equation: Substitute the slope and the point into the point-slope form equation.\newlineUsing the point (7,7)(7, 7) and the slope 23\frac{2}{3}, we substitute into the equation:\newliney−7=(23)(x−7)y - 7 = \left(\frac{2}{3}\right)(x - 7)
  4. Check for Simplification: Check the equation for any possible simplification. The equation y−7=23(x−7)y - 7 = \frac{2}{3}(x - 7) is already in the correct form and does not require further simplification.

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