To find the equation of a line with a given slope and y-intercept, we can use the slope-intercept form. The slope-intercept form of a line is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept
Given:
- Slope [tex]\( m = -1 \)[/tex]
- Y-intercept [tex]\( b = -5 \)[/tex]
Substitute the given values into the slope-intercept form:
[tex]\[ y = -1x - 5 \][/tex]
This simplifies to:
[tex]\[ y = -x - 5 \][/tex]
So, the equation of the line with a slope of -1 and a y-intercept of -5 is:
[tex]\[ y = -x - 5 \][/tex]
Now, let's compare this with the given options:
A. [tex]\( y = -5x - 1 \)[/tex]
B. [tex]\( y = -x + 5 \)[/tex]
C. [tex]\( y = -5x + 1 \)[/tex]
D. [tex]\( y = -x - 5 \)[/tex]
The correct matching option is:
[tex]\[ \boxed{D} \][/tex]
