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