To find the equation of a line with a given slope and y-intercept, we can use the slope-intercept form of the equation of a line, which is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, which is the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0.
Given:
- The slope [tex]\( m = \frac{1}{4} \)[/tex].
- The y-intercept [tex]\( b = 2 \)[/tex].
Let's substitute these values into the slope-intercept form equation.
[tex]\[ y = \left(\frac{1}{4}\right)x + 2 \][/tex]
So, the equation of the line with a slope of [tex]\(\frac{1}{4}\)[/tex] and a y-intercept of 2 is:
[tex]\[ y = \left(\frac{1}{4}\right)x + 2 \][/tex]
Thus, the equation of the line is:
[tex]\[ y = (0.25)x + 2 \][/tex]
This is the required equation of the line.
