Write  an  equation  in  slope­intercept  form  for  the  line  that  satisfies  each  set  of  conditions.    9. passes  through  (­6,  15),  parallel  to  the  graph  of  3x  +  2y  =  1  10. passes  through  (5,  ­2),  perpendicular  to  the  graph  of  x  +  2y  =  8

parallel lines have the same slope

3x+2y =1

solve for y to find the slope

subtract 3x

2y = -3x+1

divide by 2

y = -2/3 x+1/2

slope is -2/3

point slope form is

y-y1 = m(x-x1)

y-15 = -2/3 (x--6)

y-15 = -2/3 (x+6)

distribute

y-15=-2/3x-4

add 15 to each side

y = -2/3 x +11  

this is in slope intercept form

10. passes through (5, ­2), perpendicular to the graph of x + 2y = 8

perpendicular lines have negative reciprocal slopes

x+2y=8

subtract x

2y = -x+8

divide by 2

y = -1/2 x +4

-1/2  becomes 2

the new slope is 2

point slope form is

y-y1 = m(x-x1)

y--2 = 2(x-5)

y+2 = 2x-10

subtract 2  from each side

y = 2x-12

this is in slope intercept form