Question

Consider the line y=4x-4.

Answer 1

9514 1404 393

Answer:

• parallel: y = 4x -6
• perpendicular: y = -1/4x +27/4

Step-by-step explanation:

If we want the new line to be written in slope-intercept form, we need to find the new value of the y-intercept. The equation of the line is ...

  y = mx +b . . . . . . . for slope m and y-intercept b

Solving for b gives ...

  b = y -mx . . . . . . . subtract mx from both sides.

The values of x and y come from the point we want the line to pass through. The value of m will be the same for the parallel line as for the given line: 4. For the perpendicular line, it will be the opposite reciprocal of this: -1/4.

Parallel line

  b = 6 -4(3) = 6 -12 = -6

  y = 4x -6

Perpendicular line

  b = 6 -(-1/4)(3) = 6 +3/4 = 27/4

  y = -1/4x +27/4