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A line passes through #(9 ,2 )# and #( 3, 8 )#. A second line passes through #( 4, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

(3 , 2 )

The first step is to calculate the gradient of the line passing through the 2 given points , using the #color(blue)" gradient formula " #

# m = (y_2 - y_1)/(x_2 - x_1) #

where #(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "#

let # (x_1,y_1)=(9,2)" and " (x_2,y_2)=(3,8)#

#rArr m = (8-2)/(3-9) = 6/(-6) = - 1 #

There are an infinite number of points that will lie on the same line as (4,1) with a gradient of -1

However , by the definition of gradient , from (4,1) , move 1 to the left and 1 up ( which means subtract 1 from x-coord and add 1 to the y-coord ) you will get a point on the line.

hence (4,1) →(4-1,1+1) → (3,2) is a point on the same line. other points may be found in the same way.

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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.