A line passes through $(4, 3)$ $(4 ,3 )$ and $(7, 1)$ $(7 ,1 )$ . A second line passes through $(1, 1)$ $(1 ,1 )$ . 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 $(4, 3)$ $(4 ,3 )$ and $(7, 1)$ $(7 ,1 )$ . A second line passes through $(1, 1)$ $(1 ,1 )$ . 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 · 2018-05-01T06:12:00

The two lines have the same slope because they are parallel.

One point on the second line is $(\frac{3}{2}, 2)$ $(3/2,2)$ .

Explanation:

In order to solve this question, we need to find the slope of the first line. The second will have the same slope, since they are parallel.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$
$= \frac{1 - 3}{7 - 4} = - \frac{2}{3}$ $=(1-3)/(7-4)=-2/3$

If we write the equation of the second line as:

$y = m x + c$ $y=mx+c$ we can substitute in the value of $m$ $m$ :

$y = \frac{2}{3} x + c$ $y=2/3x+c$

We can substitute in the point $(1, 1)$ $(1,1)$ to find the value of $c$ $c$ :

$1 = \frac{2}{3} (1) + c$ $1=2/3(1)+c$

$c = \frac{1}{3}$ $c=1/3$

So $y = \frac{2}{3} x + \frac{1}{3}$ $y=2/3x+1/3$

Any point that we can substitute into this equation that makes it true is a point on that line. Let's choose $y = 2$ $y=2$ and find the value of $x$ $x$ that makes the equation too:

$2 = \frac{2}{3} x + \frac{1}{3}$ $2=2/3x+1/3$

$x = \frac{3}{2}$ $x=3/2$

One point on the second line, then, is $(\frac{3}{2}, 2)$ $(3/2,2)$ .

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A line passes through $(4, 3)$ $(4 ,3 )$ and $(7, 1)$ $(7 ,1 )$ . A second line passes through $(1, 1)$ $(1 ,1 )$ . 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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Impact of this question

Science

Math

Humanities

... and beyond

A line passes through (4,3)(4 ,3 ) and (7,1)(7 ,1 ). A second line passes through (1,1)(1 ,1 ). 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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Impact of this question

A line passes through $(4, 3)$ $(4 ,3 )$ and $(7, 1)$ $(7 ,1 )$ . A second line passes through $(1, 1)$ $(1 ,1 )$ . What is one other point that the second line may pass through if it is parallel to the first line?