What's the equation of a line that passes through points (0, -1) and (2,3)?

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Answer 1 · 2016-12-13T00:15:43

#y = 2x - 1#

First, we need to determine the slope of the line. The formula for determining the slope of a line is:

#color(red)(m = (y_2 - y_1)/(x_2 - x_1))# where #m# is the slope and the x and y terms are for the points: #(x_1,y_1)# and #(x_2,y_2)#

For this problem the slope is:

#m = (3 - -1)/(2 - 0)#

#m = (3 + 1)/2#

#m = 4/2#

#m = 2#

Now, selecting one of the points we can use the point slope formula to find the equation.

The point slope formula is:

#color(red)(y - y_1 = m(x - x_1)#

Substituting one of our points gives:

#y - -1 = 2(x - 0)#

#y + 1 = 2x#

Solving for #y# to put this in standard form gives:

#y + 1 - 1 = 2x - 1#

#y + 0 = 2x - 1#

#y = 2x - 1#