To find the slope-intercept form of an equation for a line that is parallel to the given line [tex]\( y = 2x - 3 \)[/tex], we follow these steps:
1. Identify the slope of the given line:
The equation of the given line is in slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept. For the line [tex]\( y = 2x - 3 \)[/tex], the slope [tex]\( m \)[/tex] is 2.
2. Determine the slope of the parallel line:
Lines that are parallel have the same slope. Therefore, the slope of the line parallel to [tex]\( y = 2x - 3 \)[/tex] is also 2.
3. Construct the equation of the parallel line:
The general form of the equation of a line in slope-intercept form is [tex]\( y = mx + b \)[/tex]. We already know the slope [tex]\( m \)[/tex] is 2, so the equation of the parallel line will be [tex]\( y = 2x + b \)[/tex].
4. Determine the y-intercept [tex]\( b \)[/tex]:
Since the problem doesn't specify any additional points that the line passes through, we can use any value for the y-intercept [tex]\( b \)[/tex].
To summarize, the slope-intercept form of the equation for any line that is parallel to [tex]\( y = 2x - 3 \)[/tex] can be written as [tex]\( y = 2x + b \)[/tex], where [tex]\( b \)[/tex] is the variable y-intercept.
If a specific point through which the parallel line passes was provided, you would substitute that point's coordinates into [tex]\( y = 2x + b \)[/tex] to determine the specific value of [tex]\( b \)[/tex]. Since no specific point is mentioned in this problem, we leave [tex]\( b \)[/tex] as an undefined constant.
