What is the slope-intercept form of the line passing through # (-1, 4) # and # (-4, 2)#?
The line's equation is: 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.
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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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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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