What is the equation of the line that goes through #(- 5,4)# and #( 2,8)#?

Answer 1

#y=4/7x+48/7#

The line is probably linear, and so it is given by:

#y=mx+b#
#m# is the slope of the line
#b# is the y-intercept
The slope #m# is found by:
#m=(y_2-y_1)/(x_2-x_1)#, where #(x_1,y_1)# and #(x_2,y_2)# are the two coordinates.

So here:

#m=(8-4)/(2-(-5))#
#=4/7#

So, the equation is:

#y=4/7x+b#
Now, we plug in any of the two coordinates' #x# and #y# values into the equation, and we will get the #b# value. I'll choose the first coordinate.
#:.4=4/7*-5+b#
#4=-20/7+b#
#b=4+20/7#
#=48/7#
#:.y=4/7x+48/7#

Trying for the second coordinate:

#8=4/7*2+48/7#
#8=8/7+48/7#
#8=56/7#
#8=8# (CORRECT!)
Indeed, the line is #y=4/7x+48/7#. Here is its graph:

graph{4/7x+48/7 [-10, 10, -5, 5]}

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Answer 2

The equation of the line that passes through the points (-5,4) and (2,8) is:

[ y = \frac{4-8}{-5-2} (x - (-5)) + 4 ]

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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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