To find the equation of the line in the form [tex]\( y = 4x + b \)[/tex], we need to determine the value of the y-intercept [tex]\( b \)[/tex].
Step-by-Step Solution:
1. Understand the Line Equation: The general form of the line equation given is [tex]\( y = 4x + b \)[/tex].
2. Substitute the Given Point: We are given a specific value for [tex]\( y \)[/tex], which is 3. This substitution occurs in the equation of the line [tex]\( y = 4x + b \)[/tex].
3. Solve for [tex]\( b \)[/tex]:
- Insert [tex]\( y = 3 \)[/tex] into the equation [tex]\( y = 4x + b \)[/tex]:
[tex]\[
3 = 4x + b
\][/tex]
4. Assuming [tex]\( x = 0 \)[/tex]: To determine the y-intercept (where the line crosses the y-axis), we typically consider the point where [tex]\( x = 0 \)[/tex]. This simplifies the equation, as the [tex]\( x \)[/tex]-term becomes 0:
- If [tex]\( x = 0 \)[/tex]:
[tex]\[
3 = 4(0) + b
\][/tex]
- Simplify this to:
[tex]\[
3 = b
\][/tex]
Hence, the value of the y-intercept [tex]\( b \)[/tex] is 3.
So, the complete equation of the line is:
[tex]\[
y = 4x + 3
\][/tex]
