To find the equation of a line when given the slope and the y-intercept, we use the slope-intercept form of the equation of a line, which is:
[tex]\[ y = mx + b \][/tex]
In this form:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept of the line.
From the problem, we are given:
- The slope [tex]\( m = -3 \)[/tex]
- The y-intercept [tex]\( b = 4 \)[/tex]
Substitute the given values into the slope-intercept form equation:
[tex]\[ y = -3x + 4 \][/tex]
Now, we match this with one of the given options:
A. [tex]\( y = 4x + 3 \)[/tex] (not correct, the slope and y-intercept do not match)
B. [tex]\( y = -3x - 4 \)[/tex] (not correct, the y-intercept is wrong)
C. [tex]\( y = 4x - 3 \)[/tex] (not correct, both the slope and y-intercept are wrong)
D. [tex]\( y = -3x + 4 \)[/tex] (correct, matches our equation)
Therefore, the correct option is:
D. [tex]\( y = -3x + 4 \)[/tex]
