To find the equation of a line given a point on the line and the slope, we use the slope-intercept form of the equation of a line, which is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Given:
- The slope [tex]\( m = 3 \)[/tex]
- A point [tex]\( (-3, -5) \)[/tex] that lies on the line
We need to find the y-intercept [tex]\( b \)[/tex]. To do this, we substitute the given point [tex]\( (x, y) \)[/tex] into the equation:
[tex]\[ y = mx + b \][/tex]
Plugging in the values, we get:
[tex]\[ -5 = 3(-3) + b \][/tex]
Now solve for [tex]\( b \)[/tex]:
[tex]\[ -5 = -9 + b \][/tex]
Add 9 to both sides:
[tex]\[ -5 + 9 = b \][/tex]
[tex]\[ b = 4 \][/tex]
So the y-intercept [tex]\( b \)[/tex] is 4. Therefore, the equation of the line is:
[tex]\[ y = 3x + 4 \][/tex]
Thus, the correct answer is:
A. [tex]\( y = 3x + 4 \)[/tex]
