What is the slope-intercept form of the line passing through # (-1, 4) # and # (-4, 2)#?

Answer 1

The line's equation is:
#y = (2/3) x + (14/3)#

Hence the y-axis intercept is 14/3
and the slope is 2/3.

slope is calculated as y / x.

Change in x = (-1) - (-4) = 3 and change in y = 4 - 2 = 2 apply to the points on the line at (-1,4) and (-4,2).

Thus, slope = m = 2/3.

A line has the equation y = m x + c, where c is the y-axis intercept. Starting at the first point, x = -1 and y = 4, we get 4 = (2/3) (-1) + c, which becomes c = 4 + (2/3) = 14/3.

The line's equation is: #y = (2/3) x + (14/3)#
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Answer 2

To find the slope-intercept form of the line passing through the points (-1, 4) and (-4, 2), first calculate the slope using the formula:

[ m = \frac{y_2 - y_1}{x_2 - x_1} ]

Substitute the coordinates of the points into the formula:

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

Now that we have the slope, we can use the point-slope form of a linear equation:

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

Substitute the coordinates of one of the points and the calculated slope into the equation:

[ y - 4 = \frac{2}{3}(x - (-1)) ]

[ y - 4 = \frac{2}{3}(x + 1) ]

To convert to slope-intercept form, distribute the slope:

[ y - 4 = \frac{2}{3}x + \frac{2}{3} ]

[ y = \frac{2}{3}x + \frac{2}{3} + 4 ]

[ y = \frac{2}{3}x + \frac{14}{3} ]

So, the slope-intercept form of the line passing through the points (-1, 4) and (-4, 2) is ( y = \frac{2}{3}x + \frac{14}{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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