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How do you write an equation of a line that contains (5, 7) and (-3, 11)?

Answer 1

#x+2y=19#

The slope of a line through #(5,7)# and #(-3,11)# is given by the relation:
#color(white)("XXX")color(green)m=(Deltay)/(Deltax)=(11-7)/((-3)-5)=color(green)(-1/2)#

The slope-point form for a line with slope #color(green)m# through a point #(color(red)a,color(blue)b)# is
#color(white)("XXX")y-color(blue)b=color(green)m(x-color(red)a)#

Using #color(green)(m=-1/2)# as the slope and
#(color(red)a,color(blue)b)=(color(red)5,color(blue)7)# as a point,
we have:
#color(white)("XXX")y-color(blue)7=color(green)(-1/2)(x-color(red)5)#

While this could be considered a valid solution to the given question,
it is normal to convert this into standard form:

#color(white)("XXX")2y-14=-x+5#

#color(white)("XXX")x+2y=19#

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Answer 2

Hazel Anglin

The equation of the line passing through the points (5, 7) and (-3, 11) is (y = -\frac{1}{2}x + \frac{17}{2}).

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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.