What is the equation of the line between #(0,2)# and #(25,-10)#?

1 Answer
Jun 25, 2017

The equation of the line is #y = -12/25 * x + 2#

Explanation:

The equation of a line is based on two simple questions: "How much #y# changes when you add #1# to #x#?" and "How much is #y# when #x=0#?"

First, it's important to know that a linear equation has a general formula defined by #y = m*x + n#.

Having those questions in mind, we can find the slope (#m#) of the line, that is how much #y# changes when you add #1# to #x#:

#m = (D_y)/(D_x)#, with #D_x# being the difference in #x# and #D_y# being the difference in #y#.

#D_x = 0-(25) = 0 - 25 = -25#
#D_y = 2-(-10) = 2+10 = 12#

#m = -12/25#

Now, we need to find #y_0#, that is the value of #y# when #x=0#. Since we have the point #(0,2)#, we know #n = y_0 = 2#.

We now have the slope and the #y_0# (or #n#) value, we apply in the main formula of a linear equation:

#y = m*x + n = -12/25 * x + 2#