Sure, let’s work through the problem step-by-step to find the equation that represents Nolan’s line.
1. Identify the y-intercept:
- Nolan plots the [tex]$y$[/tex]-intercept at [tex]$(0,3)$[/tex]. The y-intercept is the point where the line crosses the y-axis, and this gives us the constant term, [tex]$b$[/tex], in the equation of the line.
2. Determine the slope:
- The slope given is [tex]$2$[/tex]. The slope represents the steepness of the line and is denoted as [tex]$m$[/tex] in the equation of the line.
3. Form the equation of the line:
- The general 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.
4. Substitute the slope and y-intercept into the equation:
- Here, [tex]$m = 2$[/tex] and [tex]$b = 3$[/tex]. Substituting these values in, we get:
[tex]\[
y = 2x + 3
\][/tex]
5. Verify the result:
- We have successfully formed the equation of the line using the provided slope and y-intercept.
Thus, the equation that represents Nolan's line is:
[tex]\[
y = 2x + 3
\][/tex]
Among the given options, the correct choice is:
[tex]\[
\boxed{y = 2x + 3}
\][/tex]
