A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

It can be any point on the second line, for example (0,10) as explained below.

The slope of the line passing though (9,2) and (3,5) would be #(5-2)/(3-9)= (3)/(-6) = -1/2#.
The slope of the second line would also be #- 1/2# because it is parallel to the first one. Second line also passes through the point (4,8), hence its equation in point slope form would be #y-8= -1/2 (x-4)#. Another point on this line can be any, which can be obtained by assigning any arbitrary value to x and finding the corresponding y. For example, let x=0, then y=10. Hence this point point would be (0,10)
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Answer 2

To find a point that the second line may pass through if it is parallel to the first line, we can use the concept that parallel lines have the same slope.

The slope of the first line passing through the points (9, 2) and (3, 5) can be calculated using the formula: [ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ] [ m = \frac{{5 - 2}}{{3 - 9}} ] [ m = \frac{{3}}{{-6}} ] [ m = -\frac{1}{2} ]

Since the second line is parallel to the first line, it must have the same slope. Now, we can use the slope-intercept form of a line (y = mx + b) and substitute the slope (-1/2) and one of the given points (4, 8) to find the y-intercept (b).

[ 8 = -\frac{1}{2}(4) + b ] [ 8 = -2 + b ] [ b = 10 ]

Now we have the slope (-1/2) and the y-intercept (10). We can use this information to find another point on the second line. Let's choose another x-coordinate, say 0, and use it to find the corresponding y-coordinate.

[ y = -\frac{1}{2}(0) + 10 ] [ y = 10 ]

So, another point that the second line may pass through is (0, 10).

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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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