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compare the slope of the line joining the two points together against the slope of the objective function
Jun 13th, 2015

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Straight lines will be parallel if they have the same slope. There is no limit then to the number of lines with slope 2:

But there will be only one line with slope 2 that passes through a given point, such as (1, −3). In other words, a line will be determined by its slope and the coördinates of one point on it.  How can we find the equation of that line?

Problem 1. To a is the slope of the line.

We are given that a = 2.  Therefore, the equation will look like this:

y  =  2x + b.

We must now determine b.

To do that, we must use the information that (1, −3) are the coördinates of a point on the line.  Those coördinates then solve the equation.

−3  =  2· 1 + b

This implies

b  =  −5.

The equation of the line is

y  =  2x − 5.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 13th, 2015

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