# section 10.1 notes

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Section 10.1 Notes. Definition of Inclination. The inclination of a nonhorizontal line is the positive angle (less than or 180) measured counterclockwise from the x -axis to the line. Horizontal Line. y. = 0 or 0. x. Vertical Line. y. x. Obtuse Angle. y. . x. - PowerPoint PPT Presentation

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Section 10.1 NotesDefinition of InclinationThe inclination of a nonhorizontal line is thepositive angle (less than or 180) measuredcounterclockwise from the x-axis to the line.yx = 0 or 0Horizontal LineVertical Line

xyObtuse AnglexyAcute Anglexy

(x1, 0)(x2, y1)

Inclination and SlopeIf a nonvertical line has inclination and slope m, thenm = tan Look at the graphs of an acute angle and an obtuse angle. What is the sign of the slope of the line that has an angle of inclination that is acute? What is the sign of the slope of the line that has an angle of inclination that is obtuse?The sign of the slope of the line that has an angle of inclination that is acute is always positive. This means that the tangent of an acute angle is always positive.The sign of the slope of the line that has an angle of inclination that is obtuse is always negative. This means that the tangent of an obtuse angle is always negative.

Example 1Graph and find the inclination of the line given by 5x y + 3 = 0 to the nearest thousandth of a radian.

5x y + 3 = 0y = 5x + 3 m = 5tan = 5 = 1.373 rad.Two distinct lines in a plane are either parallel or intersecting. If they intersect and are not perpendicular, their intersection forms two pairs of vertical angles. One pair is acute and the other pair is obtuse. The smaller of these angles is the angle between the two lines.

Angle Between Two LinesIf two nonperpendicular lines have slopes m1 and m2. The angle between the two lines is found by

xym2m1The tan must be positive since is always an acute angle thus the reason for the absolute value sign in the formula.Example 2Graph and find the angle between the following two lines to the nearest thousandth of a radian.Line 1: 2x + y = 4Line 2: x y = 2

Line 1: 2x + y = 4Line 2: x y = 2m1 = -2m2 = 12x + y = 4x y = 2