What is the slope of any line parallel to the line 9x + 4y = 7 ?

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hala718 eNotes educator | Certified Educator

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Given the line:

9x + 4y = 7

We need to determine the slope of any line that is parallel to the line 9x+4y=7.

We know that the slopes of two parallel lines are equal.

Then, we will determine the slope of the given line.

First, we will need to rewrite the equation of the line in the standard form.

==> 9x + 4y = 7

==> 4y = -9x + 7

==>  y= (-9/4) x + 7/4

The slope is x's coefficient which is -9/4

Then, the slope of any parallel line is -9/4.

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justaguide eNotes educator | Certified Educator

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The slope of parallel lines are equal.

SO if we can find the slope of the line 9x + 4y = 7, we know the slope of any line parallel to it.

Now we rewrite the equation in the form y = mx + c, where m is the slope and c is the y-intercept.

9x + 4y = 7

=> 4y = 7 - 9x

=> y = 7/4 - (9/4)x

=> (-9/4)x + 7/4

So m = -9/4

Therefore the required slope is -9/4

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