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Write the equation of the line that passes through the points (4,6) and (2,7). 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 (4,6) (4,6) and (2,7) (2,7) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

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Q. Write the equation of the line that passes through the points (4,6) (4,6) and (2,7) (2,7) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate slope: Calculate the slope of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Given points: (4,6)(4,6) and (2,7)(2,7), where (x1,y1)=(4,6)(x_1, y_1) = (4, 6) and (x2,y2)=(2,7)(x_2, y_2) = (2, 7). Slope (mm) = 7−62−4=1−2=−12\frac{7 - 6}{2 - 4} = \frac{1}{-2} = -\frac{1}{2}.
  2. Given points: Use the point-slope form of the equation of a line, which is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineWe can use either of the two points for (x1,y1)(x_1, y_1). Let's use the point (4,6)(4,6).\newlinePoint-slope form: y−6=−12(x−4)y - 6 = -\frac{1}{2}(x - 4).

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