To write the equation of a line given the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( (0, b) \)[/tex], we use the slope-intercept form of a line, which is:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] is the slope, and [tex]\( b \)[/tex] is the y-intercept.
Given:
- Slope [tex]\( m = 7 \)[/tex]
- Y-intercept [tex]\( b = -4 \)[/tex]
Substitute these values into the slope-intercept equation:
[tex]\[ y = 7x - 4 \][/tex]
Thus, the equation of the line is [tex]\( y = 7x - 4 \)[/tex].
Looking at the choices given in the question, the correct answer is:
D. [tex]\( y = 7x - 4 \)[/tex]
The other options available are:
A. [tex]\( y = 4x - 7 \)[/tex]
B. [tex]\( y = -7x + 4 \)[/tex]
C. [tex]\( y = -4x + 7 \)[/tex]
These do not match the derived equation of the line with the given slope and y-intercept. Therefore, option D, [tex]\( y = 7x - 4 \)[/tex], is the correct answer.
