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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
b = −5.
The equation of the line is
y = 2x − 5.
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