Question 53

What is the equation of the line passing through the point (2,-3) and making an angle of -45°with the positive X-axis?

Solution

Slope of line making an angle of -45° with the positive x-axis = $$tan (-45$$°$$) = -tan (45$$°$$) = -1$$

Equation of line passing through $$(x_1,y_1)$$ and making slope $$m$$ is $$(y - y_1) = m (x - x_1)$$

Equation of line passing through (2,-3) and slope = -1

=> $$(y + 3) = -1(x - 2)$$

=> $$y + 3 = -x + 2$$

=> $$x + y = 2 - 3 = -1$$

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