What is the equation of the line between #(-17,14)# and #(19,6)#?

Answer 1

# y = -2/9x + 92/2#

First, we find the slope #m# of the line. The slope of the line is the change in #y# per unit of change in #x#. Equivalently, this means that a line with slope #a/b# will rise #a# units as #x# increases by #b# units. Then, we can find the slope from two points with the following formula:
#m = ("change in "y)/("change in "x) = (y_2-y_1)/(x_2-x_1)#

In this case, that gives us

#m = (6-14)/(19 - (-17)) = -8/36 = -2/9#
Now, we can write the equation using the point-slope form of a line. #y - y_1 = m(x - x_1)#
Picking either of the points will work, so let's use #(19, 6)# (as an exercise, verify that this gives the same result if you use the other point). This gives us the equation
#y - 6 = -2/9(x - 19)#
If we wish to put that into the more common slope-intercept form, we can just multiply it out and solve for #y#.
#y - 6 = -2/9x + 38/9#
# y = -2/9x + 92/2#
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Answer 2

The equation of the line passing through the points (-17, 14) and (19, 6) is ( y = -\frac{1}{3}x + \frac{80}{3} ).

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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.

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.

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.

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.

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