To determine the equations of the lines that are parallel to the given line, we first need to identify the slope of that line. The standard form of a linear equation is y = mx + b, where m represents the slope and b is the y-intercept.
In the equation y = 3x + 5, the slope m is 3. For two lines to be parallel, they must have the same slope. Therefore, any line parallel to this one must also have a slope of 3.
Given this information, the general form of the equations for lines parallel to y = 3x + 5 can be expressed as:
- y = 3x + c, where c is any real number.
This means that you can choose any value for c to create different lines that are parallel to the original line. For example, if c = 0, the equation would be:
- y = 3x
Choosing c = -2, the equation becomes:
- y = 3x – 2
So, to find all equations of lines parallel to y = 3x + 5, simply maintain the slope of 3 and adjust the y-intercept.