What's the equation of a line that passes through (1,2) (3,5)?

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Answer 1 · 2015-06-26T23:13:13

In slope-intercept form, the equation of the line is:

#y = 3/2x + 1/2#

as derived below...

First let's determine the slope #m# of the line.

If a line passes through two points #(x_1, y_1)# and #(x_2, y_2)# then its slope #m# is given by the formula:

#m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)#

In our example, #(x_1, y_1) = (1, 2)# and #(x_2, y_2) = (3, 5)#, so

#m = (y_2 - y_1)/(x_2 - x_1) = (5 - 2)/(3 - 1) = 3/2#

In slope-intercept form, the line has the equation:

#y = mx + c# where #m# is the slope and #c# the intercept.

We know #m=3/2#, but what about #c#?

If we substitute the values for #(x, y) = (1, 2)# and #m = 3/2# into the equation, we get:

#2 = (3/2)*1 + c = 3/2+c#

Subtract #3/2# from both sides to get:

#c = 2 - 3/2 = 1/2#

So the equation of the line can be written:

#y = 3/2x + 1/2#