To determine which equation represents Nolan's line, we need to understand the components given in the problem and how they translate into the equation of a line in slope-intercept form.
1. Identify the slope and the y-intercept:
- The y-intercept of the line is given as [tex]\( (0, 3) \)[/tex]. This means that when [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] equals 3.
- The slope of the line is given as 2. The slope [tex]\( m \)[/tex] describes how much [tex]\( y \)[/tex] increases for each increase of 1 unit in [tex]\( x \)[/tex].
2. Slope-Intercept Form:
- The slope-intercept form of a line is given by:
[tex]\[
y = mx + b
\][/tex]
where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept
3. Substituting the known values:
- Here, the slope [tex]\( m = 2 \)[/tex] and the y-intercept [tex]\( b = 3 \)[/tex].
- Substituting these values into the slope-intercept form, we get the equation:
[tex]\[
y = 2x + 3
\][/tex]
4. Conclusion:
- Among the given options, the equation that represents Nolan's line is:
[tex]\[
y = 2x + 3
\][/tex]
Thus, the equation that represents Nolan's line is:
[tex]\[ \boxed{y = 2x + 3} \][/tex]
