How do you write the equation in slope intercept form given (2, 2), (-1, 4)?

Answer 1

The slope-intercept form of the equation is #y=-2/3x+10/3#

The slope-intercept form of the equation of the line is #y=mx+b# where #m=# slope and #b=# the y intercept
#m=(y_2-y_1)/(x_2-x_1)#
#x_1=2# #y_1=2# #x_2=-1# #y_2=4#
#m = (4-2)/(-1-2)#
#m = (2)/(-3)#
#m=-2/3#

Now use the point slope formula to solve for the equation of the line.

#(y-y_1)=m(x-x_1)#
For this situation we are given the slope of #3# and a point of #(2,1)#
#m=-2/3# #x_1=2# #y_1=2#
#(y-y_1)=m(x-x_1)#
#(y-2)=-2/3(x-2)#
#y-2=-2/3x-4/3#
#y cancel(-2) cancel(+2)=-2/3x+4/3 + 2#
#y=-2/3x+4/3 +6/3#
#y=-2/3x+10/3#
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Answer 2

#y = (-2x)/3 +10/3#

If you have two points on a straight line, there is a lovely formula which allows you to get the equation immediately. It is based on the formula for the slope, so you kill two birds with one stone!

#(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)#
#(y-2)/(x-2) = (4-2)/(-1-2) = 2/-3 " this value is the slope"#
#(y-2)/(x-2) = -2/3" cross multiply"#
#3y - 6 = -2x +4#
#3y = -2x +10#
#y = (-2x)/3 +10/3#
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Answer 3

First, find the slope using the formula: (m = \frac{{y_2 - y_1}}{{x_2 - x_1}})

Substitute the coordinates ((x_1, y_1) = (2, 2)) and ((x_2, y_2) = (-1, 4)) into the formula:

(m = \frac{{4 - 2}}{{-1 - 2}} = \frac{2}{-3})

Next, use one of the given points and the slope to find the equation in slope-intercept form (y = mx + b). Let's use ((2, 2)):

(2 = \frac{2}{-3}(2) + b)

Solve for (b):

(2 = \frac{4}{-3} + b)

(b = 2 + \frac{4}{3})

(b = \frac{6}{3} + \frac{4}{3})

(b = \frac{10}{3})

So, the equation in slope-intercept form is (y = -\frac{2}{3}x + \frac{10}{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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