Final answer:
An equation that represents a line parallel to 3y−2x=−24 is any line with the same slope of 2/3. Hence, equations of the form y=(2/3)x+c, with any real number c, would be parallel to the original line.
Step-by-step explanation:
To find an equation that represents a line which is parallel to the line given by the equation 3y−2x=−24, we must first convert this equation into slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. For the equation 3y−2x=−24, we can rearrange it to y=mx+b form by solving for y:
- Divide every term by 3: y = (2/3)x + 8
The slope of this line is 2/3. A line parallel to this one must have the same slope. Therefore, any equation of the form y=(2/3)x+c, where c is any real number, represents a line parallel to the original line. The value of c will determine the y-intercept of the new line, but it will not affect the parallel nature of the lines since the slopes are identical.