Verify if the lines y = 7x/2 - 17/2 and y = 14x/9 - 24/9 are parallel .Verify if the lines y = 7x/2 - 17/2 and y = 14x/9 - 24/9 are parallel.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You may also use the following approach, hence, since the given form of equations of lines is the slope intercept form, `y = mx + b` (m slope, b - y intercept), you may find the slopes of the lines `d_1, d_2` such that:

`m_1 = 7/2, m_2 = 7/2`

Hence, since the slopes of the given lines are equal `m_1 = m_2 = 7/2` , the lines are parallel, `d_1 || d_2` .

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To prove that the lines d1 and d2 are parallel we'll have to verify if the system formed from the equations of d1 and d2 has not any solutions.

We'll put the equation of the lines in the general form:

ax + by + c = 0

The first equation is:

7x-2y-17=0

The second equation is:

14x-9y-24=0

We'll form the system:

7x-2y-17=0

We'll add 17 both sides:

7x - 2y = 17 (1)

14x-9y-24=0

We'll add 24 both sides:

14x - 9y = 24 (2)

We'll solve the system using elimination method. For this reason, we'll multiply (2) by -2 and we'll add the resulting equation to (1):

-14x + 4y = -34 (3)

(1) + (3): 14x - 9y - 14x + 4y = 24 - 34

We'll eliminate and combine like terms:

-5y = -10

We'll divide by -5:

y = 2

We'll substitute y in (1):

14x - 9y = 24

14x - 18 = 24

14x = 24 + 18

14x = 42

7x = 21

x = 3

The system has a solution that represents the intercepting point of the lines: (3,2). The given lines are not parallel but they are intercepting.

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