Line 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?A) 1/2 B) -2 C) 2 D) -1/2 E) 0

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have two lines, one passing through (-2,0) and (0,a) and the other passing through (4,0) and (6,2)

Now the line through (-2,0) and (0,a) is y-0 = [(a-0)/(0+2)] (x+2).

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

The slope of this line is a/2.

The other line is

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

=> y= (2/2)(x-4)

The slope of this line is 1

As the two lines are parallel, the slope has to be equal.

Therefore a/2 = 1 => a = 2

The required value of a is 2. The correct option is C.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The lines d1 and  d2 passes through  (-2,0) and (0,a) ;  and  (4,0) and (6,2).

The slope m of the lines passing through (x1,y1) and (x2, y2) is given by:

m = (y2-y1)/(x2-x1).

So the slope m1 of the line d1 is given by:

m1 =  (a-0)/(0-(-2)) = a/2.

The slope m2 of the line d2 is given by:

m2 = (2-0)/(6-4) = 2/2 = 1.

So if d1 and d2 are ||, then  their slopes should be equal.

So m1 = m2 .

Or a/2 = 1. So a = 2.

Therefore if a = 2, the  lines d1 and d2 are parallel.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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