Final answer:
The equation of the line perpendicular to 3x - 2y = -7 and passing through (-6,0) is y = -\(\frac{2}{3}\)x - 4. Hence, the correct choice is B) y = -\(\frac{2}{3}\)x - 4.
Step-by-step explanation:
To find the equation of the line that is perpendicular to the given line 3x - 2y = -7 and passes through the point (-6,0), we first need to find the slope of the given line. We can rewrite the given equation in slope-intercept form. Isolating y, we have:
y = \(\frac{3}{2}x + \frac{7}{2}\)
Here, the slope of the given line is \(\frac{3}{2}\). A line perpendicular to this line would have a slope that is the negative reciprocal. Hence, the slope of the perpendicular line is -\(\frac{2}{3}\).
Next, we use the point-slope form of the line equation, which is y - y1 = m(x - x1), where (x1,y1) is the point the line passes through and m is the slope. Substituting the point (-6,0) and the slope -\(\frac{2}{3}\), we get:
y = -\(\frac{2}{3}\)x - 4
The correct equation in slope-intercept form is:
y = -\(\frac{2}{3}\)x - 4
Therefore, the correct answer among the options given is B) y = -\(\frac{2}{3}\)x - 4.