A line passes through $(4, 7)$ $(4 ,7 )$ and $(2, 8)$ $(2 ,8 )$ . A second line passes through $(1, 5)$ $(1 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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A line passes through $(4, 7)$ $(4 ,7 )$ and $(2, 8)$ $(2 ,8 )$ . A second line passes through $(1, 5)$ $(1 ,5 )$ . 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 · 2016-06-20T14:26:40

The point $(0, \frac{11}{2})$ $(0, 11/2)$ .

Explanation:

The equation of a line is $y = m x + q$ $y=mx+q$
The line that passes from $(4, 7)$ $(4,7)$ and $(2, 8)$ $(2,8)$ can be obtained substituting the coordinates as $x$ $x$ and $y$ $y$ and doing the system

$7 = 4 m + q$ $7=4m+q$
$8 = 2 m + q$ $8=2m+q$

We can subtract the second from the first to remove $q$ $q$ obtaining

$7-8=4m-2m+\cancel(q)-\cancel(q)$

$-1=2m$ and $m=-1/2$ .

We can also calculate $q$ , even if it is not relevant for our problem, using one of the two equations

$7=-1/2*4+q$

$7=-2+q$

$q=9$

The equation of the first line is then

$y=-1/2x+9$

The second line is parallel, it means that the slope is the same $-1/2$ .
So the equation of the parallel is

$y=-1/2x+r$ where $r$ is the intercept of the second line. To find it we know that the line passes from $(1,5)$ , then

$5=-1/2*1+r$

$5+1/2=r$

$11/2=r$

The equation of the parallel is

$y=-1/2x+11/2$ .

To find another point in this line it is enough to give a value to $x$ and calculate the $y$ .
For example $x=0$ , $y=-1/2*0+11/2=11/2$ , then the point $(0, 11/2)$ is another point of the parallel.

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A line passes through $(4, 7)$ $(4 ,7 )$ and $(2, 8)$ $(2 ,8 )$ . A second line passes through $(1, 5)$ $(1 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A line passes through (4 ,7 )(4,7)(4 ,7 ) and (2 ,8 )(2,8)(2 ,8 ). A second line passes through (1 ,5 )(1,5)(1 ,5 ). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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A line passes through $(4, 7)$ $(4 ,7 )$ and $(2, 8)$ $(2 ,8 )$ . A second line passes through $(1, 5)$ $(1 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?