Let's find the equation representing Nolan's line step-by-step.
1. Identifying the y-intercept and the slope:
- Nolan plots the y-intercept of the line at [tex]\( (0, 3) \)[/tex]. This means the line crosses the y-axis at [tex]\( y = 3 \)[/tex].
- The slope of the line is given as [tex]\( 2 \)[/tex].
2. Formulating the equation of the line:
- The standard form of the equation of a line is:
[tex]\[
y = mx + b
\][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- From the given information:
- The slope [tex]\( m = 2 \)[/tex]
- The y-intercept [tex]\( b = 3 \)[/tex]
3. Substituting the values:
- Substitute [tex]\( m = 2 \)[/tex] and [tex]\( b = 3 \)[/tex] into the standard form equation:
[tex]\[
y = 2x + 3
\][/tex]
4. Finding the correct equation among the given options:
- The correct equation that represents Nolan's line is therefore:
[tex]\[
y = 2x + 3
\][/tex]
So the correct answer is:
[tex]\[
\boxed{y = 2x + 3}
\][/tex]
