Question

Write the equations for the line parallel and the line perpendicular to the given line passing through the given point.

Answer 1

Answer:

10. y=2x+1                                              y = -1/2x +1

11. y=-1/3x +6                                          y = 3x -4

12. y=-5x-18                                            y=1/5x + 14/5

Step-by-step explanation:

To write the equation of a line we must have a slope and a point. To find the slope, we use the slope from the equations for parallel lines and modify it for perpendicular lines.

10. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.   The slope here is 2. The parallel slope is 2 and the perpendicular slope is the negative reciprocal or -1/2.

Parallel                                           Perpendicular

(y-1)=2(x-0)                                       (y-1)==-1/2(x-0)          

y-1=2x                                              y-1 = -1/2 x

y=2x+1                                              y = -1/2x +1

11. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.   The slope here is -1/3. The parallel slope is -1/3 and the perpendicular slope is the negative reciprocal or 3.

Parallel                                           Perpendicular

(y-5)=-1/3(x-3)                                        (y-5)=3(x-3)          

y-5=-1/3x+1                                            y-5 = 3x - 9

y=-1/3x +6                                              y = 3x -4

12. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.   The slope here is -5. The parallel slope is -5 and the perpendicular slope is the negative reciprocal or 1/5.

Parallel                                           Perpendicular

(y-2)=-5(x--4)                                           (y-2)=1/5(x--4)          

y-2=-5(x+4)                                              y-2 = 1/5(x +4)

y-2=-5x -20                                              y-2 = 1/5x +4/5

y=-5x-18                                                    y=1/5x + 14/5