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What is the equation of the line between #(10,23)# and #(-1,0)#?

Answer 1

#y = 2.1x + 2#

The first step here is finding the gradient. We do this by dividing the difference in #y# (vertical) by the difference in #x# (horizontal). To find the difference, you simply take the original value of #x# or #y# from the final value (use the coordinates for this)

#(0 - 23)/(-1 - 10)# #= (-23)/-11# #= 2.1# (to 1dp)

We can then find the #y# intercept with the formula:

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

Where #m# is the gradient, #y_1# is a #y# value substituted from one of the two coordinates and #x_1# is an #x# value from one of the coordinates you were given (it can be from either of the two as long as it is from the same coordinate as your #y# one).

So, let's use the first coordinate, #(10,23)# as they are both positive (so it will be easier to calculate).

#m=2.1 " "##y_1 = 23 " "# and #" "x_1 = 10#

When we substitute this in, we get:

#y - 23 = 2.1 (x - 10)# #y - 23 = 2.1x - 21# #y = 2.1x + 2#

So, your line equation is:

#y = 2.1x + 2#

Hope this helps; let me know if I can do anything else:)

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Answer 2

Eva Abramson

The equation of the line is ( y = \frac{23}{11}x + \frac{107}{11} ).

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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.