How do you write an equation of a line going through (-1,2), (3,-4)?

Answer 1

#y - 2 = -3/2(x + 1)#

or

#y = -3/2x + 1/2#

To find a linear equation for the line going through these two points we can use the point-slope formula.

However, first we need to determine the slope of the line.

The slope can be found by using the formula: #color(red)(m = (y_2 - y_1)/(x_2 - x_1)# Where #m# is the slope and (#color(red)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points.
Substituting the two points given in the problem we can solve for #m# as:
#m = (-4 - 2)/(3 - (-1))#
#m = -6/4 = (2/2)(-3/2) = 1(-3/2)#
#m = -3/2#

Now that we have the slope we can use the slope-point formula to write the equation for the line.

The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))# Where #color(red)(m)# is the slope and (#color(red)((x_1, y_1))#) is a point the line passes through.
Substituting the slope of #-3/2# and using the point #(-1, 2)# we can get the equation of the line as:
#y - 2 = -3/2(x - (-1))#
#y - 2 = -3/2(x + 1)#
If we want this in the slope-intercept for we can solve for #y# as follows:
#y - 2 = -3/2x - (3/2 * 1)#
#y - 2 = -3/2x - 3/2#
#y - 2 + 2 = -3/2x - 3/2 + 2#
#y - 0 = -3/2x - 3/2 + 2#
#y = -3/2x - 3/2 + 2#
#y = -3/2x - 3/2 + 2(2/2)#
#y = -3/2x - 3/2 + 4/2#
#y = -3/2x + 1/2#
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Answer 2

To write the equation of a line going through the points (-1,2) and (3,-4), first find the slope (m) using the formula (m = \frac{y_2 - y_1}{x_2 - x_1}). Substituting the given points, (m = \frac{-4 - 2}{3 - (-1)} = \frac{-6}{4} = -\frac{3}{2}).

With the slope and one of the points, use the point-slope form of the line equation, (y - y_1 = m(x - x_1)), substituting the slope and either point. Using (-1,2), the equation is (y - 2 = -\frac{3}{2}(x + 1)).

Expanding and simplifying gives (y - 2 = -\frac{3}{2}x - \frac{3}{2}), and then adding 2 to both sides results in (y = -\frac{3}{2}x + \frac{1}{2}). So, the equation of the line is (y = -\frac{3}{2}x + \frac{1}{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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