Thank you for the opportunity to help you with your question!

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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