How do you write an equation in slope intercept form given that the line passes through the points (1,5) and (0,0)?

Question

1361 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-20T07:42:39

#y = 5x + 0#

First calculate the slope.

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

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

To avoid negative values, I will swap the order of the two points given in the question, and let #(x_1, y_1) = (0, 0)# and #(x_2, y_2) = (1, 5)#

Then:

#m = (5 - 0) / (1 - 0) = 5/1 = 5#

So the equation of the line in slope-intercept form must be:

#y = 5x+c#

for some constant #c# - which is the #y# coordinate of the intercept with the #y# axis.

This equation of the line must be satisfied by any point on the line, so we have:

#y_1 = 5x_1 + c#

That is:

#0 = (5*0) + c#

So #c = 0# and the equation of the line can be written:

#y = 5x + 0#