What is the slope-intercept form of the line passing through #(2, 2) # and #(-1, 4) #?

Answer 1

#-2/3# is the slope and #10/3# is the intercept.

An equation is followed by a line in the plane.

#y=mx+q#. In this equation we want to calculate the two parameters #m# and #q#. To do it we substitute the values of #x# and #y# and we have a system of equations
#2=2m+q# #4=-1m+q#

I write one variable as the other from one of the two equations (let's say the first):

#2=2m+q# then #q=2-2m#

and now enter this in the other formula.

#4=-m+q# then #4=-m+2-2m# #4=2-3m# #4-2=-3m# #2=-3m# #m=-2/3#
to find #q# I take the #q=2-2m# and substitute the value of #m#
#q=2-2(-2/3)=2+4/3=10/3#

There is an equation on the line.

#y=-2/3x+10/3# where #-2/3# is the slope and #10/3# is the intercept.
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Answer 2

To find the slope-intercept form of the line passing through the points (2, 2) and (-1, 4), first find the slope using the formula ( m = \frac{{y2 - y1}}{{x2 - x1}} ), then use the point-slope form ( y - y1 = m(x - x1) ) to derive the slope-intercept form. After calculations, the equation in slope-intercept form is ( y = -\frac{1}{3}x + \frac{8}{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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