parallel linesLine d1 passes through the points (-2,0) and (0,a). Line d2 passes through the points (4,0) and (6,2). What value of a makes the two lines parallel?

1 Answer

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll put the equations of the 2 lines in the standard form.

y = mx + n

m is the slope of the line

n is the y intercept

For d1 and d2 to be parallel, their slopes have to be equal.

m1 = m2

We'll write the equation of the line d1 that passes through (-2,0) and (0,a).

(0+2)/(x+2) = (a-0)/(y-0)

2/(x+2) = a/y

We'll cross multiply and we'll get:

a(x+2) = 2y

We'll remove the brackets and we'll use the symmetric property:

2y = ax + 2a

We'll divide by 2:

y = ax/2 + a

m1 = a/2

We'll write the equation of the line d2 that passes throug the points (4,0) and (6,2):

(6-4)/(x-4) = (2-0)/(y-0)

2/(x-4) = 2/y

We'll divide by 2 and we'll cross multiply and we'll get:

x - 4 = y

We'll use the symmetric property:

y = x - 4

m2 = 1

The condition for d1|| d2:

m1 = m2

a/2 = 1

a = 2