What is the y-intercept of the line perpendicular to the line y = 3/4x + 3 that includes the point (3, 1)?

a. -5/4

b. 3

c. -13/4

d. 5

  D.  5

Step-by-step explanation:

The attached shows a graph of the line in point-slope form. It has a y-intercept of 5.

The slope of the given line is 3/4. The slope of the perpendicular line will be the negative reciprocal of that: -1/(3/4) = -4/3.

The point-slope form of the equation of a line with slope m through point (h, k) can be written ...

  y = m(x -h) +k

For the desired slope and given point, this equation is ...

  y = (-4/3)(x -3) +1 = (-4/3)x +4 +1

  y = (-4/3)x +5 . . . . . equation in slope-intercept form

The y-intercept is seen to be 5.

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step-by-step explanation: