To determine the equation of Nolan’s line, we need to follow these steps:
1. Identify the slope and y-intercept.
- The y-intercept is given as the point [tex]\((0, 3)\)[/tex]. This means when [tex]\(x = 0\)[/tex], [tex]\(y = 3\)[/tex].
- The slope of the line is given as [tex]\(2\)[/tex].
2. Understand the slope-intercept form of a line.
- The slope-intercept form of the equation of a line is [tex]\(y = mx + b\)[/tex] where:
- [tex]\(m\)[/tex] is the slope.
- [tex]\(b\)[/tex] is the y-intercept.
3. Substitute the given values into the slope-intercept form.
- Here, the slope [tex]\(m\)[/tex] is [tex]\(2\)[/tex].
- The y-intercept [tex]\(b\)[/tex] is [tex]\(3\)[/tex].
Substituting these into the equation [tex]\(y = mx + b\)[/tex], we get:
[tex]\[ y = 2x + 3 \][/tex]
4. Match the derived equation to the options provided.
- The options are:
1. [tex]\(y = 2x + 1\)[/tex]
2. [tex]\(y = 2x + 3\)[/tex]
3. [tex]\(y = 3x + 2\)[/tex]
4. [tex]\(y = 3x + 5\)[/tex]
The correct equation that represents Nolan's line is:
[tex]\[ y = 2x + 3 \][/tex]
Therefore, the answer is:
[tex]\[ \boxed{2} \][/tex]
