A line passes through $(3, 2)$ $(3 ,2 )$ and $(7, 3)$ $(7 ,3 )$ . A second line passes through $(1, 4)$ $(1 , 4 )$ . 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 · 2016-03-18T12:01:47

$(- 15, 0)$ $(-15,0)$

Slope of line passing through say $A (3, 2)$ $A(3,2)$ and $B (7, 3)$ $B(7,3)$ is $\frac{3 - 2}{7 - 3} = \frac{1}{4}$ $(3-2)/(7-3)=1/4$

As such any line parallel to $A B$ $AB$ will have a slope of $\frac{1}{4}$ $1/4$ .

Let us point slope form to find equation of line passing through $(1, 4)$ $(1,4)$ and having a slope of $\frac{1}{4}$ $1/4$ , which is

$(y - 4) = \frac{1}{4} (x - 1)$ $(y-4)=1/4(x-1)$ or

$4 (y - 4) = (x - 1)$ $4(y-4)=(x-1)$ or $4 y - 16 = x - 1$ $4y-16=x-1$ or

$x - 4 y + 15 = 0$ $x-4y+15=0$

One point on line $x - 4 y + 15 = 0$ $x-4y+15=0$ could be, say if $y = 0$ $y=0$ , $x = - 15$ $x=-15$ i.e.

$(- 15, 0)$ $(-15,0)$

A line passes through (3,2)(3 ,2 ) and (7,3)(7 ,3 ). A second line passes through (1,4)(1 , 4 ). What is one other point that the second line may pass through if it is parallel to the first line?