How do you write the equation of the line passing through the points (3,4) and (1,-6)?

1 Answer
EZ as pi
Jun 24, 2016

#y = 5x - 11#

Explanation:

There are several methods to choose from:

Method 1. Use the given points to find the gradient, then substitute one of the points as (x,y) as well as the slope (m), into #y = mx+c# to find the value of #c#.
Then substitute the values of m and c to find the final equation.

Method 2. Make simultaneous equations using each point as an (x,y) but with m and c as the unknowns. Solve for m and c and substitute them into #y = mx + c#

Method 3. There is a neat formula for exactly this case. "Find the equation if you are given two points". Quick and easy!

#(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1) " for " (3,4) and (1,-6)#

#(y-(-6))/(x-1) = (4-(-6))/(3-1) = 10/2 = 5/1#

#(y+6)/(x-1) = 5/1" cross multiply and re-arrange"#

#y + 6 =5x - 5#

#y = 5x - 5-6#
#y = 5x - 11#

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