A line passes through $(4, 9)$ $(4 ,9 )$ and $(2, 7)$ $(2 ,7 )$ . A second line passes through $(2, 6)$ $(2 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

Question

1405 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-31T13:45:28

Parallel means the slope is equal. Therefore we must find the slope of the first two points.

The formula for slope is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2 - y_1)/(x_2 - x_1)$

$m = \frac{7 - 9}{2 - 4}$ $m = (7 - 9)/(2 - 4)$

$m = - \frac{2}{- 2}$ $m = -2/-2$

$m = 1$ $m = 1$

Now, we use point slope form to insert the other point.

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

$y - 6 = 1 (x - 2)$ $y - 6 = 1(x - 2)$

$y - 6 = x - 2$ $y - 6 = x - 2$

$y = x + 4$ $y = x + 4$

Any two points ${x, y}$ ${x, y}$ satisfy this equation are on your desired line. For example, (-3, 1) is a point on this line.

Hopefully this helps!

A line passes through (4,9)(4 ,9 ) and (2,7)(2 ,7 ). A second line passes through (2,6)(2 ,6 ). What is one other point that the second line may pass through if it is parallel to the first line?