What is the equation of the line that goes through point (3,-1) and has a slope = -1?

Answer 1

Use the point-slope form, #y - y_1 = m(x - x_1)#

Substitute #3# for #x_1#, #-1# for #y_1#, and #-1# for #m#.
#y - (-1) = (-1)(x - 3)#
#y + 1 = (-1)(x - 3)#
Distribute the #-1# through the parentheses:
#y + 1 = 3 - x#
Subtract #1# from both sides:
#y = 2 - x#

Done

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Answer 2

Using the point-slope form of a linear equation, where ( m ) is the slope and ( (x_1, y_1) ) is a point on the line, the equation of the line passing through the point (3, -1) with a slope of -1 is:

[ y - y_1 = m(x - x_1) ]

[ y - (-1) = -1(x - 3) ]

[ y + 1 = -x + 3 ]

[ y = -x + 2 ]

So, the equation of the line is ( y = -x + 2 ).

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Answer 3

The equation of a line in slope-intercept form is ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.

Given that the slope ( m = -1 ) and the point ( (3, -1) ) lies on the line, we can substitute these values into the equation.

[ y = -1x + b ]

Now, substitute the coordinates of the point ( (3, -1) ) into the equation to find ( b ).

[ -1 = -1(3) + b ]

[ -1 = -3 + b ]

[ b = 2 ]

Now that we have found the value of ( b ), substitute it back into the equation to get the final equation of the line.

[ y = -x + 2 ]

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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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