A line passes through $(4, 9)$ $(4 ,9 )$ and $(1, 6)$ $(1 ,6 )$ . A second line passes through $(3, 7)$ $(3 ,7 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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A line passes through $(4, 9)$ $(4 ,9 )$ and $(1, 6)$ $(1 ,6 )$ . A second line passes through $(3, 7)$ $(3 ,7 )$ . 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 · 2016-10-25T15:50:31

(0,4)

Explanation:

First of all, both of the lines are parallel to each other, meaning they have the same slope

To find the slope, we use the slope formula:

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

Plug in the numbers from the points of the 2 lines, and find the slope of both lines

$\frac{9 - 6}{4 - 1} = \frac{3}{3} = 1$ $(9-6)/(4-1) = 3/3 = 1$

The 1 is the slope of both of the lines, as parallel lines have the same slope.

Now, we can use the point-slope formula to get the slope-intercept equation of the second line

$y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$

Plug in the numbers, and get the new formula

$y - 7 = 1 (x - 3)$ $y-7=1(x-3)$
$y - 7 = x - 3$ $y-7=x-3$
$y = x + 4$ $y=x+4$

Now, we can get a second point for the second line: the y-intercept. To find the y-intercept, plug in 0 for the x value of the equation, and simplify. The resulting point found should be your new answer:

$(0, 4)$ $(0,4)$

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A line passes through $(4, 9)$ $(4 ,9 )$ and $(1, 6)$ $(1 ,6 )$ . A second line passes through $(3, 7)$ $(3 ,7 )$ . 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 (4,9)(4 ,9 ) and (1,6)(1 ,6 ). A second line passes through (3,7)(3 ,7 ). 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 $(4, 9)$ $(4 ,9 )$ and $(1, 6)$ $(1 ,6 )$ . A second line passes through $(3, 7)$ $(3 ,7 )$ . What is one other point that the second line may pass through if it is parallel to the first line?