Through $(1, 7)$ $(1,7)$ ; parallel to the line passing through $(2, 5)$ $(2,5)$ and $(- 2, 1)$ $(-2,1)$ ?

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Answer 1 · 2018-01-20T01:56:04

First, calculate what the slope of a line through $(2, 5)$ $(2, 5)$ and $(- 2, 1)$ $(-2, 1)$ would be.

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

$m = \frac{5 - 1}{2 - (- 2)}$ $m = (5 - 1)/(2 - (-2))$

$m = 1$ $color(red)m = 1$

A line parallel to this must have the same slope.

$y = 1 x + b$ $y = color(red)1x + b$

$y = x + b$ $y = x + b$

We can now substitute in our known point $(1, 7)$ $(color(green)1, color(blue)7)$ to find the $y$ $y$ -intercept.

$7 = 1 + b$ $color(blue)7 = color(green) 1 + b$

$6 = b$ $6 = b$

And now, we can write the equation of this line as we know both the slope and the $y$ $y$ -intercept.

$y = x + 6$ $y = x + 6$

Through (1,7)(1,7); parallel to the line passing through (2,5)(2,5) and (−2,1)(-2,1)?