Question

1.What is the equation of the line perpendicular to  that passes through ? Write your answer in slope-intercept form. Show your work.

Answer 1

1. Use a compass to make arc marks which intersect above and below then connect.

2.
`y=(1)/(3)x + 2`

Explanation:

1. To construct a perpendicular line, use a compass to draw arc marks from one end of the segment through point P. Then repeat this again at the other end. This means at point P there will be two intersecting arc marks. Repeat the process down below with the same radius as used above. Then connect the two intersections.

2. The point slope form of a line is
`(y-y_1)=m(x-x_1)` where
`x_1=-3\\y_1=1`. We write

`(y-1)=m(x--3)\\(y-1)=m(x+3)`

Since the line is to be perpendicular to the line shown it will have the negative reciprocal to the slope of the function 3x+y =-8. To find m, rearrange the function to be y=-8-3x. The slope is -3 and the negative reciprocal will be 1/3.

`(y-1)=(1)/(3)(x+3)`

Simplify for slope intercept form.

`(y-1)=(1)/(3)(x+3)\\(y-1)=(1)/(3)x+1\\y=(1)/(3)x + 2`