College Algebra

Question

Given two lines L1 and L2 with slopes m1= −2a−86 and m2= −7a+22, respectively, what value(s) of a will make:

(i)  L1 parallel to L2:  a= 1914​Incorrect

(ii)  L1 perpendicular to L2:   a= 

If there is more than one such value of a that will satisfy a given condition, separate multiple answers with commas. Provide exact values only.

Please help

Answer 1

(i) a=21.6

parallel lines have the same slope

m1 = m2

-2a -86 = -7a + 22

5a = 108

a= 108/5 = 21.6 = 21 3/5

(ii) m1 = -1/m2

perpendicular lines have slopes that are negative inverses of each other

-2a -86 = -1/(-7a+ 22) = 1/(7a-22)

(-2a-86)(7a-22) = 1

-14a^2 + 44a - 602a + 1892 = 1

-14a^2 -558a +1891 =0

14a^2 +558a -1891 = 0

a = -558/28 + or - (1/28)sqr(558^2 +4(14)(1891))

=exactly (-558+sqr(417260))/28, (-558-sqr(417260))/28

a= approximately 3.14131 or -43.003 make L1 and L2 perpendicular

a = 3.14131, -43.003

-2(3.14131)-86 = -92.28262

7(3.14131) - 22= 21.98917-22 = -0.01083

-92.28262 x -0.01083 =0.99942 = approximately 1

-2(-43.003) -86 = 0.003

7(-43.003)-22 = -301.021-22 =- 323.021

1/-323.021 = about 0.003096

-2a-86 = -1/(-7a+22)

-2(43.003)-86 = -1(-7(43.003)+22)

0.003 = about 0.003