Line k goes through (2,3) and (4,9). write an equation of a line parallel to line k that goes through the point (4,1)

The answer is: y = 3x - 11

Step-by-step explanation:

Given points (2, 3) and (4, 9), find the slope of line k:

m = (y - y1)/(x - x1)

m = (3 - 9)/(2 - 4)

m = -6/-2 = 6/2 = 3

A parallel line has the same slope and passes through a given point. Use the point slope form of the equation and point (4, 1):

y - y1 = m(x - x1)

y - 1 = 3(x - 4)

y - 1 = 3x - 12

y = 3x - 12 + 1

y = 3x - 11

Proof using point (4, 1):

f(4) = 3(4) - 11

= 12 - 11 = 1, giving point (4, 1)

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