Final answer:
The equations y=-1/3x+4 and -2x+y=-3 are independent because they have different slopes, meaning they will intersect at exactly one point.
Step-by-step explanation:
The equations y=-1/3x+4 and -2x+y=-3 represent two lines on a cartesian plane. To determine whether these equations are dependent, independent or neither, we need to see if they represent the same line (dependent), intersect at exactly one point (independent), or are parallel and distinct (neither).
First, we need to write both equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The first equation is already in this form, with a slope of -1/3 and a y-intercept of 4. For the second equation, we rewrite it as y = 2x - 3, which has a slope of 2 and a y-intercept of -3.
Since the two lines have different slopes, they cannot be the same line (dependent) and they are not parallel (they don't have the same slope). Therefore, these lines are independent because they will intersect at exactly one point.
Answer
The equations y=-1/3x+4 and -2x+y=-3 are independent.