The equation of the perpendicular line is "y = -3/2x - 17/2", and option A) "y = -3/2x - 17" is the correct match.
To find the equation of a line perpendicular to "y = 2/3x + 4" and passing through the point (-3, -4), we need to use the fact that the slopes of perpendicular lines are negative reciprocals.
The given line has a slope of 2/3. The negative reciprocal of this slope is -3/2, which will be the slope of the perpendicular line.
Now, we can use the point-slope form of a linear equation: "y - y1 = m(x - x1)", where (x1, y1) is a point on the line, and m is the slope.
Using the point (-3, -4) and the slope -3/2, we get:
"y + 4 = -3/2(x + 3)"
Now, simplify the equation:
"y + 4 = -3/2x - 9/2"
Subtract 4 from both sides:
"y = -3/2x - 9/2 - 4"
Combining the constants:
"y = -3/2x - 17/2"
Therefore, the equation of the line perpendicular to "y = 2/3x + 4" and passing through (-3, -4) is:
"y = -3/2x - 17/2"
The question probable may be:
What is the equation of the line y = 2∕3x + 4. that is perpendicular to the line and passes through the point (-3, -4)?
A) y = -3/2x - 17
B) y = -2/3x - 6
C) y = 3/2x + 12
D) y = 2/3x - 2