To find the equation of a line in slope-intercept form, we start by understanding the slope-intercept form itself, which is given by:
[tex]\[ y = mx + b \][/tex]
Here:
- [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 problem:
- The slope ([tex]\(m\)[/tex]) is 5.
- The y-intercept ([tex]\(b\)[/tex]) is -3.
Substitute these values into the slope-intercept form equation:
[tex]\[ y = 5x + (-3) \][/tex]
This simplifies to:
[tex]\[ y = 5x - 3 \][/tex]
Now, let's compare this equation with the provided options:
A. [tex]\( y = 5x + 3 \)[/tex]
B. [tex]\( y = 5x - 3 \)[/tex]
C. [tex]\( x = 3y - 5 \)[/tex]
D. [tex]\( y = -3x + 5 \)[/tex]
The correct equation from the comparison is:
[tex]\[ \boxed{y = 5x - 3} \][/tex]
Hence, the correct option is:
[tex]\[ \boxed{B} \][/tex]
