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What is the slope of the parallel line if a line is parallel to the line for the...

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tuleen092009 | Student, Grade 11 | eNotes Newbie

Posted October 19, 2010 at 2:00 AM via web

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What is the slope of the parallel line if a line is parallel to the line for the equation: (1/2)y = (1/2)x - 9?

 

 

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neela | High School Teacher | (Level 3) Valedictorian

Posted October 19, 2010 at 2:10 AM (Answer #1)

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The given line is (1/2)y = (1/2)x -9.

We can write the equation by multiplying both sides by 2 to remove the fractional coefficients of x and y:

y = x - 9*2

y = 1*x - 18 which is in the standard form of y = mx +c . Here m is the slope and c  is the y intercept.

So the line y = x-18 has the slope 1 as the coefficient of x  is 1.

All parallel lines have the same slope.

Therefore a parallel line to y = x-18 has the slope 1.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 19, 2010 at 2:02 AM (Answer #2)

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(1/2)y = (1/2)x  - 9

To find the slope for the line first we need to rewrite the equation using the slope form:

y= mx + b

m is the slope:

==> (1/2)y = (1/2)x - 9

Mutiply the equation by 2:

==> y= x - 18

Now the equation is in the slope form:

==> The slope m = 1

Since the required line is parallel to the given line, then the slopes are equals.

==> the required slope is also m = 1

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted October 19, 2010 at 2:04 AM (Answer #3)

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The slopes of 2 parallel lines are equal.

We'll have to put the equation of the line in the standard form:

y = ax + b, where a = m is the slope and b is y intercept.

If the equation of the line is:

(1/2)y = (1/2)x - 9

We'll have to divide both sides by (1/2):

y = [(1/2)/(1/2)]x - 9*2

y = x - 18

It is obvious that m = 1 and n is -18.

The slope of the parallel line is m = 1.

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william1941 | College Teacher | (Level 3) Valedictorian

Posted October 19, 2010 at 2:04 AM (Answer #4)

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The slopes of all parallel lines are the same. Now we have the equation (1/2)y = (1/2) x - 9.

This is the equation of a line. If we write it in the form y = mx + c, can find the slope easily as in y = mx +c , m represents the slope and c is the y - intercept

Therefore:

(1/2)y = (1/2) x - 9

multiply by 2

=> y = x - 18

Therefore we get the slope of the line as 1.

The slope of the lines parallel to (1/2)y = (1/2) x - 9 is 1.

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