A line passes through $(4 ,9 )$ and $(7 ,4 )$ . A second line passes through $(8 ,7 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2016-08-07T13:51:52

$y=-5/3x+61/3$

As the two lines are parallel they both have the same gradient.

gradient (slope) $->("change in the y-axis")/("change in the x-axis")$

Let point 1 be $P_1->(x_1,y_1)=(4,9)$
Let point 2 be $P_2->(x_2,y_2)=(7,4)$

Let point 3 be $P_3->(x_3,y_3) =(8,7)$

For the first line reading left to right $->x_1 to x_2$

So gradient is $P_2-P_1 ->(y_2-y_1)/(x_2-x_1) = (4-9)/(7-4) =-5/3$

Thus the gradient is $m=-5/3$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus equation for the second line $-> y=-5/3x+c$

This passes through the point $P_3 ->(x_3,y_3) =(8,7)$

$=> y_3=-5/3x_3+c" "->" "7=-5/3(8)+c$

$=>c=7+5/3(8) = 61/3$

Thus the equation of the second line is:

$y=-5/3x+61/3$

A line passes through (4 ,9 )(4 ,9 ) and (7 ,4 )(7 ,4 ). A second line passes through (8 ,7 )(8 ,7 ). What is one other point that the second line may pass through if it is parallel to the first line?