Question

Given two lines L₁ and L₂ with slopes m₁ = − 9 a − 3/ − 8 and m₂ = − 9 a + 6 /5 , respectively, what value(s) of a will make:

L₁ parallel to L₂ : a=

Answer 1

To determine the values of a that will make line L₁ parallel to line L₂, we need to set their slopes equal to each other and solve for a. The value of a that satisfies this condition is -7/12.

Step-by-step explanation:

To determine which values of a will make line L₁ parallel to line L₂, we need to compare their slopes. The slope of L₁ is given as m₁ = -9a - 3/-8. The slope of L₂ is given as m₂ = -9a + 6/5. Two lines are parallel if and only if their slopes are equal. Therefore, we need to set the two slopes equal to each other and solve for a.

-9a - 3/-8 = -9a + 6/5

Next, we can cross-multiply to eliminate the fractions. We get: -40(-9a - 3) = -8(-9a + 6)

Expanding and simplifying the equation gives: 360a + 120 = 72a - 48

Moving all the terms involving a to one side gives: 360a - 72a = -48 - 120

Combining like terms gives: 288a = -168

Finally, we can solve for a by dividing both sides of the equation by 288: a = -168/288 = -7/12