A line passes through $(2, 8)$ $(2 ,8 )$ and $(3, 9)$ $(3 ,9 )$ . A second line passes through $(7, 4)$ $(7 ,4 )$ . 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 · 2018-06-10T20:50:07

$(0, - 3)$ $color(blue)((0,-3)$

First find the gradient of the line passing through points $(2, 8)$ $(2,8)$ and $(3, 9)$ $(3,9)$

$\frac{9 - 8}{3 - 2} = 1$ $(9-8)/(3-2)=1$

Any line parallel to this will have the same gradient.

Equation of the line passing through point $(7, 4)$ $(7,4)$ .

Using point slope form of a line:

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

Where $m$ $m$ is the gradient:

$y - 4 = (x - 7)$ $y-4=(x-7)$

$y = x - 3$ $y=x-3$

To find another point that this line passes through, we just put in a value for $x$ $bbx$ and calculate the corresponding value of $y$ $bby$ :

Let $x = 0$ $x=0$

Then:

$y = 0 - 3 = - 3$ $y=0-3=-3$

Another point is $(0, - 3)$ $(0,-3)$

The co-ordinates of a point on this line could be written:

$(x, x - 3)$ $(x, x-3)$

PLOT:

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A line passes through (2 ,8 )(2,8)(2 ,8 ) and (3 ,9 )(3,9)(3 ,9 ). A second line passes through (7 ,4 )(7,4)(7 ,4 ). What is one other point that the second line may pass through if it is parallel to the first line?