To write the equation of a line given a slope (m) and a y-intercept (b), you can use the equation of a line in slope-intercept form, which is:
[tex]\[ y = mx + b \][/tex]
Here:
- [tex]\( m \)[/tex] is the slope.
- [tex]\( b \)[/tex] is the y-intercept, which is the point where the line crosses the y-axis.
Given:
- [tex]\( m = 0 \)[/tex]
- [tex]\( b = -4 \)[/tex]
Let's substitute these values into the slope-intercept form of the equation:
[tex]\[ y = 0x + (-4) \][/tex]
Simplifying the equation:
[tex]\[ y = 0x - 4 \][/tex]
Since multiplying anything by 0 gives 0, the term [tex]\(0x\)[/tex] disappears, leaving us with:
[tex]\[ y = -4 \][/tex]
Therefore, the equation of the line is:
[tex]\[ y = -4 \][/tex]
This means that for any value of [tex]\(x\)[/tex], [tex]\(y\)[/tex] will always be [tex]\(-4\)[/tex]. The line is a horizontal line that intersects the y-axis at [tex]\(-4\)[/tex].
So, the correct equation of the line with the given slope and y-intercept is:
[tex]\[ y = -4 \][/tex]
