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How do you write the equation of the line in the form AX+BY=C if (2,5) ; m=3/1?

Answer 1

#3x-1y=1

Given the point #(2,5)# and the slope #m=3/1# we can start with the slope-point form for the line: #color(white)("XXX")(y-haty) = m(x-hatx)# or, for the given values: #color(white)("XXX")(y-5) = 3(x-2)#

Simplifying #color(white)("XXX")y-5 = 3x-6#

Rearranging so variables are on the left and constant is on the right: #color(white)("XXX")-3x + y = -1#

There is normally a requirement that #A# of #Ax+By=C# be #>=0# In this case: #color(white)("XXX")3x-1y=1#

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Answer 2

Eli Assouline

The equation of a line in the form AX + BY = C can be written using the point-slope form and then converting it to the standard form. The point-slope form is:

y - y₁ = m(x - x₁)

Substituting the given values (2, 5) for (x₁, y₁) and m = 3/1:

y - 5 = (3/1)(x - 2)

Expanding and rearranging terms:

y - 5 = 3x - 6

Bringing all terms to one side to achieve the standard form:

3x - y = 1

Therefore, the equation of the line in the form AX + BY = C is 3x - y = 1.

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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.