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

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Answer 1 · 2018-01-20T01:56:04

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

#m = (y_1 - y_2)/(x_1 - x_2)#

#m = (5 - 1)/(2 - (-2))#

#color(red)m = 1#

A line parallel to this must have the same slope.

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

#y = x + b#

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

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

#6 = b#

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

#y = x + 6#