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What is the inclination of the line that passes through the points (8,2) and (12,6)?

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braunem | Student, Grade 11 | (Level 2) eNoter

Posted March 21, 2011 at 5:06 PM via web

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What is the inclination of the line that passes through the points (8,2) and (12,6)?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted March 21, 2011 at 5:10 PM (Answer #1)

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Inclination of the line is the angle made by the line to x axis.

The inclination of the line depends on the gradient of that line.

The gradient of the line is the ratio between the changes in y direction and changes in x direction.

The inclination of the line is the slope of that line.

 m = (y2 - y1)/(x2 - x1)

We notice that the numerator and denominator represents the legs of a right triangle.

m = tan a, where a is the angle made by the line and x axis.

x1 = 8 and x2 = 12

y1 = 2 and y2 = 6

tan a = (6 - 2)/(12 - 8)

tan a = 4/4

tan a = 1

The inclination of the line with respect to x axis is the angle a = pi/4 or 45 degrees.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 21, 2011 at 5:11 PM (Answer #2)

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The slope of a line passing through the points (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1). The inclination of a line with the positive x axis is the arc tan of the slope.

Here we have the points (8, 2) and (12, 6)

The slope is (6 - 2)/(12 - 8) = 4/4 = 1

The slope of the line is 1.

The angle of inclination is arc tan 1 = pi/4

The required inclination of the line with the positive x-axis is pi/4.

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