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What is the equation of the line with slope # m= -7/6 # that passes through # (-7/12,2/3) #?

Answer 1

#84x+72y=-1#

Using the definition of slope: #color(white)("XXX")m=(Delta y)/(Delta x)# and given values: #color(white)("XXX")#slope: #m=-7/6#, #color(white)("XXX")#a point: #(-7/12,2/3)#, and using a variable point #(x,y)# on the required line:

#color(white)("XXX")-7/6=(y-2/3)/(x-(-7/12))#

Multiplying the right side by #12/12# to clear the fractions: #color(white)("XXX")-7/6 = (12y-8)/(12x+7)#

Then multiply both sides by #6(12x+7)# to clear the denominators #color(white)("XXX")-7(12x+7)=6(12y-8)#

Simplify #color(white)("XXX")-84x-49=72y-48#

Add #(84x+48)# to both sides (and flip the sides to write in standard form) #color(white)("XXX")84x+72y=-1#

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Answer 2

Julia Adams

The equation of the line with slope ( m = -\frac{7}{6} ) passing through ( \left(-\frac{7}{12}, \frac{2}{3}\right) ) is ( y = -\frac{7}{6}x + \frac{9}{4} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.