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How do you write the equation of the line in the form AX+BY=C if (-6, 6) and (3, -4)?

Answer 1

Savannah Anderson

#-2/3=10/9x+y#

We use the slope-intercept form:

#m(x-x_1)=y-y_1#

We find the slope using this formula:

#m=(x_2-x_1)/(y_2-y_1)#

#=>m=(-4-6)/(3-(-6))#

#=>m=-10/9#

We let #x_1=-6# and #y_1=6#

#=>-10/9(x-(-6))=y-6#

#=>-10/9(x+6)=y-6#

#=>-10/9x-20/3=y-6#

#=>-10/9x-2/3=y#

#=>-2/3=y+10/9x#

#=>-2/3=10/9x+y#

We see that #A=10/9#, #B=1#, and #C=-2/3#

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Answer 2

Hazel Anglin

First, find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)

m = (-4 - 6) / (3 - (-6))
m = -10 / 9
m = -10/9

Next, use the point-slope form of a linear equation:
y - y1 = m(x - x1)

Using the point (-6, 6):
y - 6 = (-10/9)(x - (-6))
y - 6 = (-10/9)(x + 6)

Multiply through by 9 to clear the fraction:
9y - 54 = -10(x + 6)
9y - 54 = -10x - 60
10x + 9y = -6

So, the equation of the line in the form Ax + By = C is 10x + 9y = -6.

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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.