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Use point-slope form to write the equation of a line that passes through the point (-8,7) with slope 2 . Answer:

Use point-slope form to write the equation of a line that passes through the point (−8,7) (-8,7) with slope 22 .\newlineAnswer:

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Full solution

Q. Use point-slope form to write the equation of a line that passes through the point (−8,7) (-8,7) with slope 22 .\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,y1x_1, y_1) given in the problem.\newlineThe slope mm is given as 22, and the point (x1,y1x_1, y_1) is given as (−8,7-8, 7).
  3. Substitute Values: Substitute the slope and the point into the point-slope form equation.\newlineUsing the slope m=2m = 2 and the point (x1,y1)=(−8,7)(x_1, y_1) = (-8, 7), we substitute these values into the point-slope form equation:\newline(y−7)=2(x−(−8))(y - 7) = 2(x - (-8))
  4. Simplify Equation: Simplify the equation.\newlineWe need to simplify the equation by distributing the slope and removing the double negative in the xx term:\newline(y−7)=2(x+8)(y - 7) = 2(x + 8)
  5. Check Final Equation: Check the final equation for any possible simplification or errors.\newlineThe equation (y−7)=2(x+8)(y - 7) = 2(x + 8) is already in the simplest form and there are no mathematical errors.

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