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

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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#