A line passes through (2 ,8 )(2,8) and (4 ,5 )(4,5). A second line passes through (3 ,5 )(3,5). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Vinay K.
Nov 28, 2016

(0,9.5) and (19/3,0)(0,9.5)and(193,0)

Explanation:

Parallel lines have same slope/gradient.

Slope of first line = mm = [(y_2 - y_1)/(x_2 - x_1)][y2−y1x2−x1]

= [(5-8)/(4-2)][5−84−2] = (-3/2)(−32)

Therefore slope of another line is too -(3/2)−(32).

Equation of another line :

(y - y_1) = m (x - x1)(y−y1)=m(x−x1)

(y - 5) = -3/2 (x - x_1)(y−5)=−32(x−x1)

2 xx (y - 5) = -3 xx (x-3)2×(y−5)=−3×(x−3)

2y - 10 = -3x +92y−10=−3x+9

2y + 3x = 192y+3x=19

Now by trial and error method we can put two values of x and yxandy such that these values satisfy the above equation. Best way is to put x = 0x=0 and y =0y=0.

So the other points could be

(0,9.5) and (19/3193, 0)

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