A line passes through $(3, 2)$ $(3 ,2 )$ and $(7, 3)$ $(7 ,3 )$ . A second line passes through $(1, 1)$ $(1 , 1 )$ . 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 · 2018-05-19T08:06:17

One other point on the second line is $5, 2$ $color(maroon)(5,2)$

Slope of a line $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2-y_1)/ (x_2-x_1)$

Slope of first line $m_{1} = \frac{3 - 2}{7 - 3} = \frac{1}{4}$ $m_1 = (3-2)/(7-3) = 1/4$

Since second line is parallel to the first line, their slopes are equal.

Therefore slope of second line $m_{2} = m_{1} = \frac{1}{4}$ $m_2 = m_1 = 1/4$

Equation of second line is given by point - slope formula

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

# y - 1 = (1/4) * (x - 1)

$4 y - 4 = x - 1$ $4y -4 = x - 1$

$x - 4 y = - 3$ $x - 4y = -3$

When $y = 2, x = 4 \cdot 2 - 3 = 5$ $y = 2, x = 4*2 - 3 = 5$

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