To determine the correct equation that represents Nolan's line, we need to recall the equation of a line in slope-intercept form, which is given by:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the y-intercept of the line.
Based on the information given:
1. The y-intercept of the line is at [tex]\( (0, 3) \)[/tex]. This means that when [tex]\( x = 0 \)[/tex], [tex]\( y = 3 \)[/tex]. Therefore, [tex]\( b = 3 \)[/tex].
2. The slope of the line is 2. This means the line rises 2 units for every 1 unit it runs horizontally. Therefore, [tex]\( m = 2 \)[/tex].
Substituting the values of [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the slope-intercept form, we get:
[tex]\[ y = 2x + 3 \][/tex]
Therefore, the equation that represents Nolan's line is:
[tex]\[ y = 2x + 3 \][/tex]
Among the given options:
- [tex]\( y = 2x + 1 \)[/tex]
- [tex]\( y = 2x + 3 \)[/tex]
- [tex]\( y = 3x + 2 \)[/tex]
- [tex]\( y = 3x + 5 \)[/tex]
The correct equation is:
[tex]\[ y = 2x + 3 \][/tex]
