13. Find the equations of the straight lines which passes through the point (2, 3) and are inclined at 45° to the
straight line x + 3y + 4 = 0.

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Step-by-step explanation:

The slope of a line is the tangent of the angle it makes with the x-axis. The given line has a slope of -1/3, so the lines we want will have slopes of ...

  m1 = tan(arctan(-1/3) +45°) = 0.5 . . . . . using a calculator

  m2 = tan(arctan(-1/3) -45°) = -2

Of course, these two lines are perpendicular to each other, so their slopes will have a product of -1: (0.5)(-2) = -1.

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We can use the point-slope form of the equation for a line to write the desired equations:

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

Line 1:

  y = 1/2(x -2) +3

  y = 1/2x +2

Line 2:

  y = -2(x -2) +3

  y = -2x +7

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step-by-step explanation: