To determine the equation of the line in slope-intercept form, we start with the given information and follow these steps:
1. Identify the slope: The slope, [tex]\( m \)[/tex], is given as [tex]\( \frac{2}{4} \)[/tex]. Simplifying this fraction, we get:
[tex]\[ m = \frac{1}{2} \][/tex]
2. Identify the y-intercept: The y-intercept, [tex]\( b \)[/tex], is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]. In this specific case, the y-intercept is provided as being 0, so:
[tex]\[ b = 0 \][/tex]
3. Write the equation in slope-intercept form: The slope-intercept form of a line's equation is:
[tex]\[ y = mx + b \][/tex]
Given the values for [tex]\( m \)[/tex] and [tex]\( b \)[/tex], we substitute them into the equation:
[tex]\[ y = \frac{1}{2}x + 0 \][/tex]
So, the equation simplifies to:
[tex]\[ y = \frac{1}{2}x \][/tex]
Thus, the full equation of the line with the provided slope and intercept is:
[tex]\[ y = \frac{1}{2}x \][/tex]
In conclusion, the equation of the line is:
[tex]\[ y = \frac{1}{2}x \][/tex]
