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Question

Is slope of a line is defined as the tangent of the angle it makes with the positive x axis or simply the x- axis I.e. both positive and negative

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Solution

What is slope of a straight line?

The tangent value of any trigonometric angle that a straight line makes with the positive direction of the x-axis in anticlockwise direction is called the slope or gradient of a straight line.

The angle of inclination of a line is the angle made by the line with the positive direction of the x-axis. It is usually measured from the positive x-axis in the anti-clockwise direction.

The slope of the line is generally denoted by ‘m’. Thus, m = tan θ. The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ. The slop of a line is positive or negative according as θ is acute or obtuse. Sine a line parallel to x-axis makes an angle of 0° with x-axis, therefore its slope is tan 0° = 0. A line parallel to y-axis that is i.e., perpendicular to x-axis makes an angle of 90° with x-axis, so its slope is tan π/2 = infinity. Also the slope of a line equally inclined with axes is 1 or -1 as it makes 45° or 135° angle with x-axis.



What is slope of a straight line?

The tangent value of any trigonometric angle that a straight line makes with the positive direction of the x-axis in anticlockwise direction is called the slope or gradient of a straight line.

The angle of inclination of a line is the angle made by the line with the positive direction of the x-axis. It is usually measured from the positive x-axis in the anti-clockwise direction.

The slope of the line is generally denoted by ‘m’. Thus, m = tan θ. The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ. The slop of a line is positive or negative according as θ is acute or obtuse. Sine a line parallel to x-axis makes an angle of 0° with x-axis, therefore its slope is tan 0° = 0. A line parallel to y-axis that is i.e., perpendicular to x-axis makes an angle of 90° with x-axis, so its slope is tan π2π2 = infinity. Also the slope of a line equally inclined with axes is 1 or -1 as it makes 45° or 135° angle with x-axis.


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