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How do you write the equation in point slope form given ( 1/2 , -1 ) , ( -2/3 , 6 )?

Answer 1

#y+1=-6(x-1/2)#

First, you need to know what the point-slope form of a line is. That is usually expressed as

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

This form of the equation of a line is the final goal. We need to find both the slope, #m#, and the point the line passes through at #(x_1,y_1)#.

To find the slope, #m#, you need to have the slope formula.

#m=(y_2-y_1)/(x_2-x_1)#

Plugging in the points you were given, we get

#m=(6-(-1))/((-2/3)-1/2)#

#m=(6+1)/(-4/6-3/6)#

#m=(7)/(-7/6)#

#m=7xx(-6/7)=-6#

The first point you were given was #(1/2,-1)#, so you can plug this in for #(x_1,y_1)# in the point-slope equation above.

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

#y-(-1)=-6(x-1/2)#

#y+1=-6(x-1/2)#

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Answer 2

Hazel Anglin

To write the equation in point-slope form given two points (1/2, -1) and (-2/3, 6), first find the slope using the formula:

slope = (change in y) / (change in x).

Then, choose one of the points and plug it into the point-slope form equation:

y - y1 = m(x - x1),

where (x1, y1) is one of the given points and m is the slope.

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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.