Answer: y = (-3/2)x + 8.
To find the equation of a line that passes through the point (−6,−2) and is parallel to the line 3x-2y=23x−2y=2, we can use the slope-intercept form of the line, which is y=mx+b, where m is the slope of the line and b is the y-intercept. Since the given line 3x-2y=23x−2y=2 is in slope-intercept form, we can directly read the value of the slope m from the equation. In this case, the slope is -3/2.
Since the line we are trying to find is parallel to the line 3x-2y=23x−2y=2, it has the same slope, which is -3/2. Therefore, we can use this value as the slope of the line we are trying to find.
To find the y-intercept of the line, we can plug the coordinates of the given point (-6, -2) and the slope (-3/2) into the slope-intercept form of the line, and solve for b. We get:
-2 = (-3/2)(-6) + b
Solving for b, we get b = 8.
Therefore, the equation of the line that passes through the point (−6,−2) and is parallel to the line 3x-2y=23x−2y=2 is y = (-3/2)x + 8.