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Complete the point-slope equation of the line (−7,6)(-7,6) through (−7,−8)(-7,-8) and Use exact numbers.

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Full solution

Q. Complete the point-slope equation of the line (−7,6)(-7,6) through (−7,−8)(-7,-8) and Use exact numbers.
  1. Calculate Slope: Find the slope of the line using the two given points.\newlineThe slope mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}\newlineLet's calculate the slope using the points (−7,6)(-7, 6) and (−7,−8)(-7, -8).\newlinem=−8−6−7−(−7)m = \frac{-8 - 6}{-7 - (-7)}
  2. Check for Division: Check for division by zero.\newlineSince the denominator (−7−(−7))(-7 - (-7)) is zero, the slope is undefined. This means the line is vertical.
  3. Write Line Equation: Write the equation of a vertical line.\newlineThe equation of a vertical line is x=a constant valuex = \text{a constant value}. Since both points have the same xx-coordinate, which is −7-7, the equation of the line is x=−7x = -7.

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