A line passes through $(8, 2)$ $(8 ,2 )$ and $(6, 7)$ $(6 ,7 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . 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 $(8, 2)$ $(8 ,2 )$ and $(6, 7)$ $(6 ,7 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . 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 · 2018-04-15T15:32:56

Any point on the line $y = \frac{23 - 5 x}{2}$ $y=(23-5x)/2$ is acceptable. For example $(1, 9)$ $(1, 9)$ is a correct answer.

Explanation:

To determine the slope, $m$ $m$ of a line we can use the formula

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

where $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ are any two distinct points on the line. Here, the two points for the first line are $(8, 2)$ $(8, 2)$ and $(6, 7)$ $(6, 7)$ so the slope of the line is

$m = \frac{7 - 2}{6 - 8} = - \frac{5}{2}$ $m=(7-2)/(6-8)=-5/2$

The second line must also abide by this slope definition, yet we only know one point on the line. Let's call the coordinates of the second point $(x, y)$ $(x, y)$ . The slope formula for the second line then gives

$m = - \frac{5}{2} = \frac{y - 4}{x - 3}$ $m=-5/2=(y-4)/(x-3)$

Let's solve this equation for y by multiplying both sides of this equation by $(x - 3)$ $(x-3)$ and then adding 4 to both sides of this equation.

$y = - \frac{5}{2} (x - 3) + 4 = - \frac{5}{2} x + \frac{15}{2} + 4 = - \frac{5}{2} x + \frac{23}{2}$ $y=-5/2(x-3)+4=-5/2x+15/2+4=-5/2x+23/2$

So our line has a slope of -5/2 and a $y$ $y$ -intercept of $\frac{23}{2}$ $23/2$ .

The problem statement asks for ANY other point on this line. This means we can pick any $x$ $x$ -value we want (except for 3) and then calculate the value of y. I'm going to choose $x = 1$ $x=1$ . If $x = 1$ $x=1$ , then

$y = - \frac{5}{2} (1) + \frac{23}{2} = \frac{18}{2} = 9$ $y=-5/2(1)+23/2=18/2=9$

So $(1, 9)$ $(1, 9)$ is a point on the second line.

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A line passes through $(8, 2)$ $(8 ,2 )$ and $(6, 7)$ $(6 ,7 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . 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

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A line passes through (8,2)(8 ,2 ) and (6,7)(6 ,7 ). A second line passes through (3,4)(3 ,4 ). 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 $(8, 2)$ $(8 ,2 )$ and $(6, 7)$ $(6 ,7 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . What is one other point that the second line may pass through if it is parallel to the first line?