Question

derive the equation of straight line passing through the point (x1, y1) having the slope M hence did use the equation of line which passes through (2, 1)with making an angle of 45 degree with the positive direction of x-axis​

Answer 1

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Answer 2

The equation of a straight line can be represented in the slope-intercept form as y = mx + b, where m is the slope of the line and b is the y-intercept. To derive the equation of a straight line passing through the point (x1, y1) with slope M, we can substitute the given values into the slope-intercept form to obtain y - y1 = M(x - x1).

To use this formula to find the equation of a line passing through (2,1) and making an angle of 45 degrees with the positive direction of the x-axis, we first note that the slope of the line is given by the tangent of the angle, which is equal to 1 since the line makes a 45-degree angle with the x-axis. Thus, we have M = 1.

Substituting this value along with the given point (x1, y1) = (2, 1) into the formula y - y1 = M(x - x1), we obtain:

y - 1 = 1(x - 2)

Simplifying this equation, we get:

y = x - 1

Therefore, the equation of the line passing through (2, 1) with an angle of 45 degrees with the positive x-axis is y = x - 1.

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