To determine the equation of a line in slope-intercept form, we use the formula:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] represents the slope of the line
- [tex]\( b \)[/tex] represents the y-intercept, which is the point where the line crosses the y-axis.
Given the slope ([tex]\( m \)[/tex]) is [tex]\( 4 \)[/tex] and the y-intercept ([tex]\( b \)[/tex]) is [tex]\( 2 \)[/tex], we can substitute these values into the slope-intercept equation.
Substituting [tex]\( m = 4 \)[/tex] and [tex]\( b = 2 \)[/tex]:
[tex]\[ y = 4x + 2 \][/tex]
Now, let's match this equation with the given choices:
A. [tex]\( x = -2x - 4 \)[/tex]
This equation is not in the correct form for a line (it should be [tex]\( y = \ldots \)[/tex]).
B. [tex]\( y = 4x - 2 \)[/tex]
This equation has the correct slope but the incorrect y-intercept.
C. [tex]\( y = 4x + 2 \)[/tex]
This equation has the correct slope and the correct y-intercept.
D. [tex]\( y = 2x + 4 \)[/tex]
This equation has an incorrect slope and y-intercept.
Therefore, the correct option is:
[tex]\[ \boxed{3} \][/tex] or Option C.
