What is the equation of the line passing through #(1,-4)# and #(4,-1)#?

1 Answer
KillerBunny
Nov 12, 2015

#y=x-5#

Explanation:

If you know that a line passes through two points, then that line is unique. If the points are #(x_1,y_1)# and #(x_2,y_2)#, then the equation for the line is

#\frac{x-x_2}{x_1-x_2} = \frac{y-y_2}{y_1-y_2}#

In your case, we have #(x_1,y_1)=(1,-4)# and #(x_2,y_2)=(4,-1)#

Plugging these values into the formula gives

#\frac{x-4}{1-4} = \frac{y-(-1)}{-4-(-1)}#

which becomes

#\frac{x-4}{cancel(-3)} = \frac{y+1}{cancel(-3)}#

Isolating the #y# term, we arrive at the form #y=x-5#

Let's verify:
our two points satisfy this equation, because the #y# coordinate is smaller than the #x# coordinate by #5# units:

#y_1=-4 = x_1-5=1-5#, and

#y_2 = -1 = x_2-5 = 4-5#

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