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Write the equation of the line that passes through the points (5,9) and (-2,-8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line. Answer:

Write the equation of the line that passes through the points (5,9) (5,9) and (−2,−8) (-2,-8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

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Full solution

Q. Write the equation of the line that passes through the points (5,9) (5,9) and (−2,−8) (-2,-8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate Slope: Given points: \newline(5,9)(5, 9) and \newline(−2,−8)(-2, -8) \newlineFind the slope of the line using the points. \newlineSlope, mm \newline=(y2−y1)/(x2−x1)= (y_2 - y_1)/(x_2 - x_1) \newline=(−8−9)/(−2−5)= (-8 - 9)/(-2 - 5) \newline=−17/−7= -17 / -7 \newline=17/7= 17 / 7 \newlineSo, m=17/7m = 17/7
  2. Choose Point: Choose one of the given points to use in the point-slope form equation. We can use either point, but for this example, let's use the point (5,9)(5, 9). The point-slope form of a line is 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.
  3. Substitute into Equation: Substitute the slope m=177m = \frac{17}{7} and the point (5,9)(5, 9) into the point-slope form equation.y−9=(177)(x−5)y - 9 = \left(\frac{17}{7}\right)(x - 5)This is the equation of the line in point-slope form.

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